Computational law is the branch of legal informatics concerned with the automation of legal reasoning. What distinguishes Computational Law systems from other instances of legal technology is their autonomy, i.e. the ability to answer legal questions without additional input from human legal experts. While there are many possible applications of Computational Law, the primary focus of work in the field today is compliance management, i.e. the development and deployment of computer systems capable of assessing, facilitating, or enforcing compliance with rules and regulations. Some systems of this sort already exist. TurboTax is a good example. And the potential is particularly significant now due to recent technological advances – including the prevalence of the Internet in human interaction and the proliferation of embedded computer systems (such as smart phones, self-driving cars, and robots). There are also applications that do not involve governmental laws. The regulations can just as well be the terms of contracts (e.g. delivery schedules, insurance covenants, real estate transactions, financial agreements). They can be the policies of corporations (e.g. constraints on travel, expenditure reporting, pricing rules). They can even be the rules of games (embodied in computer game playing systems). == History == Speculation about potential benefits to legal practice through applying methods from computational science and AI research to automate parts of the law date back at least to the middle 1940s. Further, AI and law and computational law do not seem easily separable, as perhaps most of AI research focusing on the law and its automation appears to utilize computational methods. The forms that speculation took are multiple and not all related in ways to readily show closeness to one another. This history will sketch them as they were, attempting to show relationships where they can be found to have existed. By 1949, a minor academic field aiming to incorporate electronic and computational methods to legal problems had been founded by American legal scholars, called jurimetrics. Though broadly said to be concerned with the application of the "methods of science" to the law, these methods were actually of a quite specifically defined scope. Jurimetrics was to be "concerned with such matters as the quantitative analysis of judicial behavior, the application of communication and information theory to legal expression, the use of mathematical logic in law, the retrieval of legal data by electronic and mechanical means, and the formulation of a calculus of legal predictability". These interests led in 1959 to the founding a journal, Modern Uses of Logic in Law, as a forum wherein articles would be published about the applications of techniques such as mathematical logic, engineering, statistics, etc. to the legal study and development. In 1966, this Journal was renamed as Jurimetrics. Today, however, the journal and meaning of jurimetrics seems to have broadened far beyond what would fit under the areas of applications of computers and computational methods to law. Today the journal not only publishes articles on such practices as found in computational law, but has broadened jurimetrical concerns to mean also things like the use of social science in law or the "policy implications [of] and legislative and administrative control of science". Independently in 1958, at the Conference for the Mechanization of Thought held at the National Physical Laboratory in Teddington, Middlesex, UK, the French jurist Lucien Mehl presented a paper both on the benefits of using computational methods for law and on the potential means to use such methods to automate law for a discussion that included AI luminaries like Marvin Minsky. Mehl believed that the law could by automated by two basic distinct, though not wholly separable, types of machine. These were the "documentary or information machine", which would provide the legal researcher quick access to relevant case precedents and legal scholarship, and the "consultation machine", which would be "capable of answering any question put to it over a vast field of law". The latter type of machine would be able to basically do much of a lawyer's job by simply giving the "exact answer to a [legal] problem put to it". By 1970, Mehl's first type of machine, one that would be able to retrieve information, had been accomplished but there seems to have been little consideration of further fruitful intersections between AI and legal research. There were, however, still hopes that computers could model the lawyer's thought processes through computational methods and then apply that capacity to solve legal problems, thus automating and improving legal services via increased efficiency as well as shedding light on the nature of legal reasoning. By the late 1970s, computer science and the affordability of computer technology had progressed enough that the retrieval of "legal data by electronic and mechanical means" had been achieved by machines fitting Mehl's first type and were in common use in American law firms. During this time, research focused on improving the goals of the early 1970s occurred, with programs like Taxman being worked on in order to both bring useful computer technology into the law as practical aids and to help specify the exact nature of legal concepts. Nonetheless, progress on the second type of machine, one that would more fully automate the law, remained relatively inert. Research into machines that could answer questions in the way that Mehl's consultation machine would picked up somewhat in the late 1970s and 1980s. A 1979 convention in Swansea, Wales marked the first international effort solely to focus upon applying artificial intelligence research to legal problems in order to "consider how computers can be used to discover and apply the legal norms embedded within the written sources of the law". Considerable progress on the development of the second type of machine was made in the following decade, with the development of a variety of expert systems. According to Thorne McCarty, "these systems all have the following characteristics: They do backward chaining inference from a specified goal; they ask questions to elicit information from the user; and they produce a suggested answer along with a trace of the supporting legal rules." According to Prakken and Sartor the representation of the British Nationality Act as a logic program, which introduced this approach, was "hugely influential for the development of computational representations of legislation, showing how logic programming enables intuitively appealing representations that can be directly deployed to generate automatic inferences". In 2021, this work received the Inaugural CodeX Prize as "one of the first and best-known works in computational law, and one of the most widely cited papers in the field." In a 1988 review of Anne Gardner's book An Artificial Intelligence Approach to Legal Reasoning (1987), the Harvard academic legal scholar and computer scientist Edwina Rissland wrote that "She plays, in part, the role of pioneer; artificial intelligence ("AI") techniques have not yet been widely applied to perform legal tasks. Therefore, Gardner, and this review, first describe and define the field, then demonstrate a working model in the domain of contract offer and acceptance." Eight years after the Swansea conference had passed, and still AI and law researchers merely trying to delineate the field could be described by their own kind as "pioneer[s]". In the 1990s and early 2000s more progress occurred. Computational research generated insights for law. The First International Conference on AI and the Law occurred in 1987, but it is in the 1990s and 2000s that the biannual conference began to build up steam and to delve more deeply into the issues involved with work intersecting computational methods, AI, and law. Classes began to be taught to undergraduates on the uses of computational methods to automating, understanding, and obeying the law. Further, by 2005, a team largely composed of Stanford computer scientists from the Stanford Logic group had devoted themselves to studying the uses of computational techniques to the law. Computational methods in fact advanced enough that members of the legal profession began in the 2000s to both analyze, predict and worry about the potential future of computational law and a new academic field of computational legal studies seems to be now well established. As insight into what such scholars see in the law's future due in part to computational law, here is quote from a recent conference about the "New Normal" for the legal profession: "Over the last 5 years, in the fallout of the Great Recession, the legal profession has entered the era of the New Normal. Notably, a series of forces related to technological change, globalization, and the pressure to do more with less (in both corpo
Ed (chatbot)
Ed was a chatbot co-developed by the Los Angeles Unified School District and AllHere Education. Described as a learning acceleration platform, it was the first personal assistant for students in the United States. Part of the district's Individual Acceleration Plan, it was able to interact with students both verbally and visually, offering support in 100 languages. The chatbot was launched on March 20, 2024, as part of the district's plan for academic recovery from the COVID-19 pandemic and to improve overall academic performance. Utilizing artificial intelligence, Ed organizes data and reports on grades, test scores, and attendance, creating individualized plans for each student. After the company behind it, AllHere, collapsed, the district shuttered operations of the chatbot on June 14, 2024. The firm is under investigation by the US Federal Bureau of Investigation. == History == On February 14, 2022, Alberto M. Carvalho became the Superintendent of the Los Angeles Unified School District, pledging to give the district a full academic recovery from the COVID-19 pandemic. In December 2022, he announced the Individual Acceleration Plan for the district, which aimed to provide each student with a unique progress report and help them determine if they were on track to graduate. The district faced criticism from disability advocates for its management of Individualized Education Programs, and in April 2022, the United States Department of Education announced that the district had failed to provide appropriate educational services to students with disabilities during the pandemic. The district had been grappling with significant absenteeism issues since the pandemic, which led to declining academic performance and disengagement among students. On February 17, 2023, the district issued a request for proposals to develop a fully integrated portal system. Later that year, they signed a $6 million, five-year contract with AllHere Education, a Boston-based company founded in 2016. The introduction of Ed follows the public launch of ChatGPT, which has been utilized by both teachers and students in educational settings. On August 4, 2023, during an annual address at the Walt Disney Concert Hall, Carvalho and the Los Angeles Unified School District announced the launch of Ed. The district invested $4 million into the chatbot, with Carvalho noting that this cost would be halved thanks to donor and grant funding. The chatbot was launched on March 20, 2024. Following its launch, a press conference was held to address security and technology concerns. Carvalho stated that the district had collaborated with security companies and incorporated filters to screen for threatening language. Months after its launch, AllHere Education furloughed most of its staff on June 14, citing their “current financial position” on its website as the reason. After learning about the furlough, the district terminated its dealings with AllHere Education. However, it stated its intention to bring the chatbot back in the future once officials determine the best course of action. Carvalho announced that he would appoint an independent task force to review what went wrong with AllHere Education and the chatbot. On February 25, 2026, the FBI served a search warrant on Carvalho’s home and office in connection with AllHere. The FBI also raided the LAUSD's headquarters. == Service == The chatbot was described as a personal assistant and a "one-stop shop for parents and students" who want to see information about a student's attendance and grades, as well as other resources from the district. Additionally, the application can function as an alarm clock, provide daily lunch menus from the school cafeteria, and offer updates on the location of school buses. The chatbot also helps students and parents who do not speak English as their first language by translating displayed information into approximately 100 different languages. The application can also help with submitting applications and give updates on progress and upcoming assignments. The district stated that the primary goal of Ed was to actively motivate students to complete homework and other tasks. == Reception == The chatbot received a mostly positive reception among parents and observers upon its launch. Some parents and teachers expressed caution about the technology, voicing concerns that the district's push for its implementation lacked public accountability. Rob Nelson from the University of Pennsylvania described the district's strategy as risky, saying that the release felt "like the beginning of a Clippy-level disaster". After the chatbot's shutdown, The 74 criticized it for misusing student data. Chris Whiteley, a former software engineer at AllHere Education, alleged that the data collected by the chatbot likely violated the district's data privacy rules.
Artificial intelligence in education
Artificial intelligence in education (often abbreviated as AIEd) is a subfield of educational technology that studies how to use artificial intelligence to create learning environments. Considerations in the field include data-driven decision-making, AI ethics, data privacy and AI literacy. Concerns include the potential for cheating, over-reliance, equity of access, reduced critical thinking, and the perpetuation of misinformation and bias. == History == Efforts to integrate AI into educational contexts have often followed technological advancement in the history of artificial intelligence. In the 1960s, educators and researchers began developing computer-based instruction systems, such as PLATO, developed by the University of Illinois. In the 1970s and 1980s, intelligent tutoring systems (ITS) were being adapted for classroom instruction. The International Artificial Intelligence in Education Society was founded in 1993. Coinciding with the AI boom of the 2020s, the use of large language models in the global north has been promoted and funded by venture capital and big tech. Companies creating AI services have targeted students and educational institutions as customers. Similarly, pre-AI boom educational companies have expanded their use of AI technologies. These commercial incentives for AIEd use may be related to a potential AI bubble. In the U.S., bipartisan support of AI development in K-12 education has been expressed, but specific implementations and best practices remain contentious. == Theory == AIEd applies theory from education studies, machine learning, and related fields. A 2019 review of the previous decade of studies found that most research prioritized technological design over pedagogical integration. Ouyang and Jiao (2021) propose three paradigms for AI in education, which follow roughly from least to most learner-centered and from requiring least to most technical complexity from the AI systems: AI-directed, learner-as-recipient: AIEd systems present a pre-set curriculum based on statistical patterns that do not adjust to learner's feedback. AI-supported, learner-as-collaborator: Systems that incorporate responsiveness to learner's feedback through, for example, natural language processing, wherein AI can support knowledge construction. AI-empowered, learner-as-leader: This model seeks to position AI as a supplement to human intelligence wherein learners take agency and AI provides consistent and actionable feedback. Some scholars place AI in education within a socio-technical framework. This positions AI alongside other emerging educational technologies, such as computing, the internet, and social media. The framework of Tsao, Heinrichs and Camit (2025) draws on new materialism and posthumanism, specifically Donna Haraway's concept of sympoiesis (making-with). This perspective views learning as an entanglement of human and non-human actors (students, teachers, and AI algorithms), where knowledge is co-composed in contact zones between human context and algorithmic prediction. AI agents have been trained on biased datasets, and thus continue to perpetuate societal biases. Since LLMs were created to produce human-like text, algorithmic bias can be introduced and reproduced. AI's data processing and monitoring reinforce neoliberal approaches to education rather than addressing inequalities. == Applications == Uses of generative AI chatbots in education have included assessment and feedback, machine translations, proof-reading exam question generation and copy editing, or as virtual assistants. Emotional AI in education is the study and development of systems that can detect learners' emotions or provide emotional support in learning. == Usage == === Schools and educators === Following the release of ChatGPT in November 2022, some schools and large school districts blocked access to the site and issued warnings that the use of such tools would be seen as cheating. Governmental and non-governmental organizations such as UNESCO, Article 4 of the European Union's AI Act, and the U.S. Department of Education have published reports advocating for specific AIEd approaches. National higher-education bodies have also published guidance on generative AI, including Ireland's Higher Education Authority, which issued a policy framework for higher education teaching and learning in December 2025. In 2024, UNESCO released updated global guidance for generative AI in education, emphasizing ethical use, teacher training, and data protection to ensure responsible integration of AI tools in learning environments. According to Taso (2025), policy implementation in higher education is interpreted and enacted differently by various organizations. These decentralized policies can lead to inconsistent enforcement and confusion among students regarding what constitutes acceptable use, with the burden of ethical navigation falling on individual teachers and students. AI integration in classrooms has created new forms of invisible labour for educators, who must navigate ambiguous policies, redesign assessments to be AI-resilient, and adjudicate potential academic integrity violations. The use of AI detection tools has also been criticised for creating an adversarial relationship between students and institutions, where students may be falsely accused of misconduct based on probabilistic software. AIEd advocates say that efforts should be made towards increasing global accessibility and training educators to serve underprivileged areas. === Students === Reliance on generative AI has been linked with reduced academic self-esteem and performance, and heightened learned helplessness. Algorithm errors and hallucinations are common flaws in AI agents, making them less trustworthy and reliable. According to a 2025 survey from Inside Higher Ed, 85% of higher education students use generative AI technology in some way, with 25% using AI to complete assignments for them. The most common reason cited for using AI to cheat was pressure to get high grades. 97% of students wanted some form of action from schools on the threat to academic integrity caused by AI, with the most popular options being clearer policies and more education about ethical uses of AI. In September 2025, The Atlantic published an op-ed from a high school senior arguing that the normalization of AI cheating was eroding critical thinking, academic integrity, creativity, and the shared student experience.
Timeline of artificial intelligence risks in global finance
The following article is a broad timeline of the course of events related to artificial intelligence risks in global finance. The AI boom has led to concerns including the existential risk from artificial intelligence, as the uptake on applications of artificial intelligence increases. By late 2025, global finance and artificial intelligence were "deeply intertwined". A June 2025 Menlo Ventures report raised concerns about the sustainability of future revenue and long-term profitability of AI, given the relatively low rate of consumer monetization. == 2017 == 30 NovemberThe New York Times said that new AI reports by McKinsey & Company, the National Bureau of Economic Research, and an AI Index created by university researchers, indicated an early AI boom. The Index built on a project—"The One Hundred Year Study on Artificial Intelligence" launched in 2014. == 2018 == 2018 was a year of incremental AI growth in finance. == 2022 == The release of ChatGPT by OpenAI became the catalyst for an artificial intelligence boom that continues to remake the global economy. According to a European Central Bank report, public interest in AI increased rapidly as evidenced with rising Google searches, AI jobs, models, patents, and innovations since late 2022. At that time Europe led the US in the size of its AI workforce. == 2023 == The regulatory body, the International Monetary Fund (IMF), published their report, "Generative Artificial Intelligence in Finance: Risk Considerations", drawing attention to oversight gaps and the need for regulations. The report explores the risks posed by using generative artificial intelligence (GenAI) systems in the financial sector including "broader risks to financial stability." == 2024 == January 12 In January 2024 Bloomberg's published its list of the "Magnificent Seven" Big Tech companies on the stock market based on their strength, size and market capitalization:Apple, Microsoft, Alphabet (Google), Amazon, Meta Platforms (Facebook), Nvidia, and Tesla. 21 June During the AI boom, Nvidia became the world's most valuable company, surpassing Microsoft, as its value increased to over US$4 trillion. In 2023 and 2024, the "Magnificent Seven" stocks were the primary drivers behind the increase in equity indexes, according to Reuters. == 2025 == === January === 23 January President Donald Trump's AI policy was announced calling for United States global leadership in artificial intelligence. The Economist noted that this politic shift in which the United States seeks "global dominance" in AI includes trimming regulations and assisting in expansion of infrastructure and increase in number of AI workers. Governments of Gulf nations were also investing trillions of dollars in AI. 27 January Against the backdrop of a tech war between China and the United States over AI dominance, within days of the launch of China's free DeepSeek App, it was the most downloaded app in the United States, rising to the first place in the Apple app store. President Trump responded immediately, saying this "sudden rise" should be a "wake-up" call to the United States, and called on US companies to be more competitive. === June === 26 June In their June 2025 report, Menlo Ventures estimated that only about 3% of consumers paid for artificial intelligence-related services, representing about $USD12 billion in annual spending. This is relatively low in contrast to the massive capital expenditure by AI infrastructure companies, which raises concerns about revenue sustainability and long-term profitability. === July === 23 July The Trump administration launched the US AI Action Plan, positioning the United States in a high-stakes technological race with China for global dominance in artificial intelligence, emphasizing that neither nation can afford to fall behind due to the exponential nature of AI advancement. The plan, a new government website and policy speech called for accelerated AI adoption across federal agencies, and a number of initiatives to make is easier for AI infrastructure expansion, and other measures to ensure American leadership in AI standards. Some leading experts warned that the administration failed to provide sufficient regulations and safeguards for AI safety. Concerns were raised about the negative impacts of cuts to research funding and tightened visa policies for scientists, potentially undermining public trust and America's ability to compete internationally. === September === 7 September The Economist cautioned that AI revenues are relatively modest compared to the high cost and investments in the creation of new data centers. Even Sam Altman, OpenAI CEO and one of the leading figures of the AI boom,, raised concerns about investors' outsized hopes for financial returns. At the same time, history has shown that new technologies, like railways and electricity, endured and spread after the initial hype faded. 12 September Economists warn that U.S. households' direct and indirect investments—mutual funds or retirement plans—in the stock market reached an unprecedented historically high level, now representing 45% of all financial assets, or about $USD51.2 trillion. Compared to the Dot-com bubble this represents a sharp increase in exposure. This makes U.S. households vulnerable to market downturns which in turn would result in decreasing consumer spending. U.S. household net worth rose to a record $176.3 trillion in the second quarter, an increase of $7.3 trillion since early 2025 and about $46 trillion higher than before the pandemic. Federal Reserve data attribute the surge primarily to gains in stock markets and housing values. However, the rise in wealth on paper coincided with increased household borrowing and growing government debt. 18 September Questions were being raised about how quickly the data centers, chips, servers, and GPUs assets of major AI companies will depreciate in value. Comparisons have been made to the Railway Mania in the aftermath of the stock market bubble where a valuable physical infrastructure remained standing, and the telecoms crash after the dot-com bubble which left fiber networks. 28 September There were warnings that record-high American stock ownership during the AI-fueled market boom is a red flag for systemic risk, as the current concentration in equities exceeds levels seen before the dot-com bubble burst in 2000, and could amplify the impact of any future stock market correction. === October === 3 October In 2025 alone, venture capitalists invested almost $USD200 billion in the artificial intelligence sector. 29 October Nvidia was the first company in the world to be valued at US$5 trillion, largely due to AI demand and strategic partnerships with leading technology and AI firms. Nvidia's increase in value was "meteoric". === November === 2 November Forbes reported that, since April, the 'Magnificent Seven' tech giants together contributed over 40% of the S&P 500's return, highlighting their outsized influence and the growing impact of AI on market valuations. CNN warned that while there is a current benefit to investors, with such a high concentration in the S&P 500, they are highly exposed to the fate of the Mag Seven. 2 November Globally there are 11,000 datacentres—huge campuses for AI infrastructure, including thousands of chips, GPUS, and servers. This represents a 500% increase over the last two decades. It is anticipated that $3USDtn more will be spent on increasing that number over the next two or three years. 5 November Concerns about the potential for a market bubble were raised as six of the AI-related Big Tech "Magnificent Seven"—that contribute to the AI boom—reported losing ground in the stock market. Global markets and artificial intelligence have become "deeply intertwined", according to a Reuters report. As of November 2025, more than 50% of the 20 largest S&P firms were deeply exposed to AI. In contrast, in 2000, the 20 S&P 500 firms represented 39% of its total value only 11 of these companies were exposed to the internet. If AI fails to deliver strong returns on their investments, these top S&P firms would be significantly impacted, according to the Economist. Analysts suggest that the AI market in 2025 may not behave like a traditional one, as investors are simultaneously aware of the risks and driven by the potential for outsized rewards. Leading AI labs may believe that the first company to achieve artificial general intelligence (AGI), when an AI system surpasses all human cognitive abilities and becomes capable of self-improvement—could dominate the future of technology and finance. While some have estimated that the potential value of such a breakthrough could be as high as $1.46 quadrillion, this figure is speculative and widely debated. 5 November Bloomberg described Nvidia's H100 Hopper-Blackwell AI chips as the "King of AI chips". Nvidia dominates the AI chip market with over 78% of the market share because of both speed and cost. According to B
Surrogate model
A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate mathematical model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (e.g., length, curvature, material, etc.). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and "what-if" analysis become impossible since they require thousands or even millions of simulation evaluations. One way of alleviating this burden is by constructing approximation models, known as surrogate models, metamodels or emulators, that mimic the behavior of the simulation model as closely as possible while being computationally cheaper to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), relying solely on the input-output behavior. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points. This approach is also known as behavioral modeling or black-box modeling, though the terminology is not always consistent. When only a single design variable is involved, the process is known as curve fitting. Though using surrogate models in lieu of experiments and simulations in engineering design is more common, surrogate modeling may be used in many other areas of science where there are expensive experiments and/or function evaluations. == Goals == The scientific challenge of surrogate modeling is the generation of a surrogate that is as accurate as possible, using as few simulation evaluations as possible. The process comprises three major steps which may be interleaved iteratively: Sample selection (also known as sequential design, optimal experimental design (OED) or active learning) Construction of the surrogate model and optimizing the model parameters (i.e., bias-variance tradeoff) Appraisal of the accuracy of the surrogate. The accuracy of the surrogate depends on the number and location of samples (expensive experiments or simulations) in the design space. A systematic data representation during training can improve model scalability, thereby reducing the need for expensive simulations. Various design of experiments (DOE) techniques cater to different sources of errors, in particular, errors due to noise in the data or errors due to an improper surrogate model. == Types of surrogate models == Popular surrogate modeling approaches are: polynomial response surfaces; kriging; more generalized Bayesian approaches; gradient-enhanced kriging (GEK); radial basis function; support vector machines; space mapping; artificial neural networks and Bayesian networks. Other methods recently explored include Fourier surrogate modeling , random forests, convolutional neural networks, and generative adversarial networks. For some problems, the nature of the true function is not known a priori, and therefore it is not clear which surrogate model will be the most accurate one. In addition, there is no consensus on how to obtain the most reliable estimates of the accuracy of a given surrogate. Many other problems have known physics properties. In these cases, physics-based surrogates such as space-mapping based models are commonly used. == Invariance properties == Recently proposed comparison-based surrogate models (e.g., ranking support vector machines) for evolutionary algorithms, such as CMA-ES, allow preservation of some invariance properties of surrogate-assisted optimizers: Invariance with respect to monotonic transformations of the function (scaling) Invariance with respect to orthogonal transformations of the search space (rotation) == Applications == An important distinction can be made between two different applications of surrogate models: design optimization and design space approximation (also known as emulation). In surrogate model-based optimization, an initial surrogate is constructed using some of the available budgets of expensive experiments and/or simulations. The remaining experiments/simulations are run for designs which the surrogate model predicts may have promising performance. The process usually takes the form of the following search/update procedure. Initial sample selection (the experiments and/or simulations to be run) Construct surrogate model Search surrogate model (the model can be searched extensively, e.g., using a genetic algorithm, as it is cheap to evaluate) Run and update experiment/simulation at new location(s) found by search and add to sample Iterate steps 2 to 4 until out of time or design is "good enough" Depending on the type of surrogate used and the complexity of the problem, the process may converge on a local or global optimum, or perhaps none at all. In design space approximation, one is not interested in finding the optimal parameter vector, but rather in the global behavior of the system. Here the surrogate is tuned to mimic the underlying model as closely as needed over the complete design space. Such surrogates are a useful, cheap way to gain insight into the global behavior of the system. Optimization can still occur as a post-processing step, although with no update procedure (see above), the optimum found cannot be validated. == Surrogate modeling software == Surrogate Modeling Toolbox (SMT: https://github.com/SMTorg/smt) is a Python package that contains a collection of surrogate modeling methods, sampling techniques, and benchmarking functions. This package provides a library of surrogate models that is simple to use and facilitates the implementation of additional methods. SMT is different from existing surrogate modeling libraries because of its emphasis on derivatives, including training derivatives used for gradient-enhanced modeling, prediction derivatives, and derivatives with respect to the training data. It also includes new surrogate models that are not available elsewhere: kriging by partial-least squares reduction and energy-minimizing spline interpolation. Python library SAMBO Optimization supports sequential optimization with arbitrary models, with tree-based models and Gaussian process models built in. Surrogates.jl is a Julia packages which offers tools like random forests, radial basis methods and kriging. == Surrogate-Assisted Evolutionary Algorithms (SAEAs) == SAEAs are an advanced class of optimization techniques that integrate evolutionary algorithms (EAs) with surrogate models. In traditional EAs, evaluating the fitness of candidate solutions often requires computationally expensive simulations or experiments. SAEAs address this challenge by building a surrogate model, which is a computationally inexpensive approximation of the objective function or constraint functions. The surrogate model serves as a substitute for the actual evaluation process during the evolutionary search. It allows the algorithm to quickly estimate the fitness of new candidate solutions, thereby reducing the number of expensive evaluations needed. This significantly speeds up the optimization process, especially in cases where the objective function evaluations are time-consuming or resource-intensive. SAEAs typically involve three main steps: (1) building the surrogate model using a set of initial sampled data points, (2) performing the evolutionary search using the surrogate model to guide the selection, crossover, and mutation operations, and (3) periodically updating the surrogate model with new data points generated during the evolutionary process to improve its accuracy. By balancing exploration (searching new areas in the solution space) and exploitation (refining known promising areas), SAEAs can efficiently find high-quality solutions to complex optimization problems. They have been successfully applied in various fields, including engineering design, machine learning, and computational finance, where traditional optimization methods may struggle due to the high computational cost of fitness evaluations.
Confusion network
A confusion network (sometimes called a word confusion network or informally known as a sausage) is a natural language processing method that combines outputs from multiple automatic speech recognition or machine translation systems. Confusion networks are simple linear directed acyclic graphs with the property that each a path from the start node to the end node goes through all the other nodes. The set of words represented by edges between two nodes is called a confusion set. In machine translation, the defining characteristic of confusion networks is that they allow multiple ambiguous inputs, deferring committal translation decisions until later stages of processing. This approach is used in the open source machine translation software Moses and the proprietary translation API in IBM Bluemix Watson.
AI data center
An AI data center is a specialized data center facility designed for the computationally intensive tasks of training and running inference for artificial intelligence (AI) and machine learning models. Unlike general-purpose data centers, they are optimized for the parallel processing demands of AI workloads, typically using hardware such as AI accelerators (e.g., GPUs, TPUs) and high-speed interconnects. The global push to construct these specialized facilities accelerated dramatically during the AI boom of the 2020s. Memory manufacturers prioritized production of High Bandwidth Memory (HBM) essential for AI servers, which led to a global memory supply shortage amid a broader competition for advanced chips, power, and infrastructure. Major tech companies are estimated to spend $650 billion on AI data centers in 2026. == Architecture == Data centers for building and running large machine learning models contain specialized computer chips, GPUs, that use 2 to 4 times as much energy as their regular CPU counterparts (250-500 watts). AI data centers use 60 or more kilowatts per server rack, whereas more standard data centers typically use 5 to 10 kilowatts per rack. == Operators == As of August 2025, The Information tracked 18 planned or existing AI data centers in the United States, operated by Amazon Web Services, CoreWeave, Crusoe, Meta, Microsoft/OpenAI, Oracle, Tesla, and xAI. Other AI data center operators include Digital Realty and Alibaba. Data centers are also being built in China, India, Europe, Saudi Arabia, and Canada. The New Yorker described CoreWeave as the most prominent AI data center operator in the United States. Two types of data center providers for machine learning have been noted: hyperscalers and neoclouds. The Verge listed large technology companies such as Google, Meta, Microsoft, Oracle and Amazon as hyperscalers. The New York Times described neoclouds as "a new generation of data center providers". CoreWeave, Nebius, Nscale, and Lambda have been described as examples of neoclouds. In January 2025, OpenAI, in partnership with Oracle and Softbank, announced the Stargate project, which as of September 2025 is composed of six built or proposed AI data centers in the United States. In response to the Stargate project, Amazon launched in October 2025 an AI data center on 1,200 acres of farmland in Indiana. This data center, known as Project Rainier, is one of the largest AI data centers in the world, with Amazon spending $11 billion on the project. Rainier is specifically intended for training and running machine learning models from Anthropic. As of that time, this facility contains seven data centers (out of an estimated 30 planned) and will use 2.2 gigawatts of electricity (equivalent to 1 million households) and millions of gallons of water per year. Computer chips from Annapurna Labs and Anthropic, Trainium 2, were designed for use in such facilities. Amazon pumped millions of gallons of water out of the ground to construct the data center, and as of June 2025, Indiana state officials are investigating whether this dewatering process led to dry wells for local residents. In November 2025, Anthropic announced a plan in partnership with Fluidstack to develop artificial intelligence infrastructure in the United States, including data centers in New York and Texas, worth $50 billion. Other AI data center projects include the Colossus supercomputer from xAI, a Louisiana-based project from Meta, Hyperion, expected to use 5 GW of power, and a second Ohio-based Meta project, Prometheus, with a capacity of 1 GW. A 3,200-acre AI data center, capable of 4.4-4.5 GW of power and located on the decommissioned Homer City Generating Station, is under construction as of 2025, and will use seven 30-acre gas generating stations supplied by EQT. As of December 2025, CRH is working on over 100 data centers in the United States. In 2025, ExxonMobil and NextEra announced plans to build a data center powered by natural gas and using carbon capture technology, with 1.2 GW of power capacity. They previously purchased 2,500 acres of land in the Southeastern United States and plan to market the data center to an artificial intelligence company. The increased interest in AI data centers has led to several executives from companies in that space becoming billionaires, including CoreWeave, QTS, Nebius, Astera Labs, Groq, Fermi (which is connected to former United States Secretary of Energy Rick Perry), Snowflake and Cipher Mining. Several companies involved in cryptocurrency mining, such as Bitdeer, CoreWeave, Cipher Mining, TeraWulf, IREN, Core Scientific, and CleanSpark have also been involved with AI data centers. == Finances == Between January and August 2024, Microsoft, Meta, Google and Amazon collectively spent $125 billion on AI data centers. Citigroup forecasted that $2.8 trillion would be spent on AI data centers by 2030, while McKinsey and Company estimated that almost $7 trillion would be spent globally by that time. According to S&P Global, $61 billion has been spent on the data center market as a whole in 2025, while debt issuance for data centers was $182 billion during the same year. Large technology companies have offloaded the financial risks of building AI data centers by setting up special purpose vehicles or by contracting with neoclouds. For example, Meta's Hyperion was mostly funded by Blue Owl Capital, which did so using a bond offering from PIMCO. Those bonds were sold to a number of clients, including BlackRock. Meta did not borrow money itself and instead established a special purpose vehicle from which it would rent the data center. This deal was structured by Morgan Stanley for $30 billion, the largest known private capital transaction as of 2025. Neoclouds such as CoreWeave have gone into debt to buy computer chips from Nvidia for their data centers, and the chips themselves have been used for loan collateral. As of December 2025, CoreWeave took out three GPU-backed loans, collectively worth $12.4 billion, from private credit firms (Blackstone, Coatue, BlackRock, PIMCO) and from banks (Goldman Sachs, JPMorgan Chase, Wells Fargo). Thus, these companies provide an indirect connection between private credit and established banks. Data centers have also established asset-backed securities, and debt for data centers has its own derivative financial products. The real estate industry, including asset managers, public companies and private investors, has also invested in data centers. == Energy sourcing == == Environmental footprint == Average AI data centers have an electricity footprint equivalent to 100,000 households, and use billions of gallons of water for cooling their hardware. In 2025, the International Energy Agency estimated that the larger AI data centers currently under construction could consume as much electricity as 2 million households. A 2024 report from the United States Department of Energy stated that data centers overall used 17 billion gallons of water per year in the United States, primarily due to "rapid proliferation of AI servers", and that this usage was forecasted to grow to nearly 80 billion gallons by 2028. Researchers estimated that AI data centers in the United States would emit 24-44 million metric tons of carbon dioxide and use 731–1,125 million cubic meters of water per year between 2024 and 2030. Peaking power plants, which have been proposed as a power source for AI data centers, emit sulfur dioxide and have historically been located disproportionately near communities of color in the United States. Reciprocating internal combustion engines, proposed as another power source for a data center, emit PM 2.5, nitrogen oxides, and volatile organic compounds. == AI data centers in the United States == In the United States, both the Biden administration and second Trump administration supported the construction of AI data centers. In January 2025, then-president Joe Biden signed an executive order for federal government agencies to support AI data centers on federal sites built by private companies, study their effect on energy prices, and encourage their use of renewable energy. In April 2025, the United States Department of Energy suggested 16 possible sites, including Los Alamos National Laboratory, Sandia National Laboratories and Oak Ridge National Laboratory. In its July 2025 AI Action Plan, the second Trump administration supported increased production of AI data centers. Several US states have incentivized local data center construction. For example, in 2024, lawmakers in Michigan approved tax breaks for data center equipment and construction material. Some data center companies have also invested or promised to invest in the infrastructure of local communities. In December 2025, Democratic senators Elizabeth Warren, Chris Van Hollen, and Richard Blumenthal wrote to seven technology companies (Google, Microsoft, Amazon, Meta, CoreWeave, Digital Realty, and Equinix) that they w