AI and data science as computational science

AI/data science is not defined by large datasets, software tools, or a particular family of algorithms.
Its central object is a reproducible computational claim connecting data, assumptions, mathematical models, algorithms, and decisions.
A serious AI/data science education must therefore integrate statistics, mathematics, computing, econometrics, and domain reasoning.

Beyond Data Processing

Data science is often described through its visible outputs: a dashboard, a prediction, a cluster of customers, a language model, or a visualization assembled from a large database. Artificial intelligence is similarly presented through its visible technologies: neural networks, generative models, autonomous agents, and software capable of performing tasks that once required human judgment.

These descriptions are not wrong, but they define a discipline by its products. A spreadsheet can contain a regression without becoming econometrics. A software package can execute a neural network without explaining why the network should be trusted. A large database can support sophisticated research, but its size does not determine the quality of the inference drawn from it.

SIAI GSB takes a more demanding position:

AI/data science should be understood as a branch of computational inquiry: the construction, execution, and criticism of formal models whose implications cannot be evaluated adequately by unaided reasoning alone.

The expression computational science has traditionally referred to the integration of applied mathematics, computer science, scientific modelling, and domain knowledge. Simulation and numerical calculation supplement theory and physical experimentation by allowing researchers to study systems that are too large, too interconnected, too costly, or too dangerous to investigate directly. The Society for Industrial and Applied Mathematics accordingly describes computational science as a multidisciplinary field and a third pillar of scientific inquiry alongside theory and experiment.

Modern AI/data science extends that tradition. Its systems may learn model components from observations instead of specifying every relationship in advance. Nevertheless, the basic discipline remains computational: represent a real process mathematically, connect the representation to data, calculate its implications, quantify uncertainty, and determine where the resulting claim may fail.

This interpretation is broader than statistics and narrower than the indiscriminate use of data. It is broader because computation, approximation, optimization, and system design affect what can be learned. It is narrower because descriptive output without a defensible inferential or decision structure is not yet computational science.

The Anatomy of a Computational Claim

Suppose a model produces an estimate, prediction, classification, or recommended decision. That output is not generated by “the data” alone. It is the result of several interacting choices:

Table 1. Components of a computational-science claim

Component	Formal role	Question that must be answered
Data	$\mathcal{D}=\{z_i\}_{i=1}^{n}$	How were the observations generated, selected, measured, and cleaned?
Assumptions	$\mathcal{H}$	Which relationships, exclusions, stability conditions, or behavioral restrictions are being imposed?
Model	$\mathcal{M}_{\theta}$	Which features of the real system are represented, and which are omitted?
Algorithm	$\mathcal{A}$	How is the model estimated, searched, optimized, or simulated?
Compute	$\mathcal{C}$	Which time, memory, hardware, and numerical-precision limits constrain the calculation?
Evaluation	$\mathcal{V}$	Against which loss function, benchmark, counterfactual, or decision criterion is success judged?

A computational result can therefore be written schematically as

where $s$ records stochastic elements such as a random seed. The notation matters because it prevents a common mistake: treating $\widehat{q}$ as if it were a fact discovered directly in the data. It is an output of an entire computational design.

Two research teams can use the same dataset and obtain different results without either making a programming error. They may encode different assumptions, choose different model classes, use different optimization procedures, stop computation at different points, or evaluate performance under different definitions of success. Reproducibility therefore requires more than sharing a final table. It requires sufficient disclosure of the complete mapping $\Phi$.

This is why AI/data science is not reducible to software development. Software engineering asks whether an implemented procedure behaves according to its specification. Computational science must also ask whether the specification is a credible representation of the process being studied.

Forward, Inverse, and Decision Problems

Many AI/data science problems can be organized around a simple system:

where $x$ denotes observed inputs, $y$ an outcome, $\theta$ unknown structural or predictive parameters, $G$ a model of the relationship, and $\varepsilon$ the variation not represented by the model.

This expression supports three distinct computational tasks.

### The forward problem

Given $x$, $\theta$, and $G$, calculate the possible outcomes:

A climate simulation, a bank stress test, or a queueing model begins largely as a forward problem. Assumptions about the system are supplied, and computation traces their implications.

### The inverse problem

Given observations of $x$ and $y$, recover an unknown parameter or function:

The loss function $\ell$ measures disagreement with the observations. The penalty $\Omega(\theta)$ discourages implausible complexity, and $\lambda$ controls that discipline. Regression, maximum likelihood, neural-network training, signal reconstruction, and many forms of causal estimation can all be viewed as inverse problems.

### The decision problem

Given a predictive distribution, select an action:

where $\mathcal{A}_{d}$ is the feasible action set and $U(a,Y)$ is the value of action $a$ under outcome $Y$.

The third task is easily neglected. A model may predict accurately without improving a decision. Conversely, a modest prediction may be highly valuable if it changes an important action at the correct margin. AI/data science becomes professionally meaningful when the forward, inverse, and decision problems are connected rather than taught as unrelated techniques.

The Error Budget

When an AI model performs poorly, “the model is wrong” is too imprecise to be useful. A computational result can fail at several layers. For a fitted function $\widehat f$ and an ideal target $f^{*}$, the excess risk can be represented schematically as

This is an organizing decomposition rather than a universal equality. It identifies five sources of failure that require different remedies:

Read as a diagnostic rather than a second scorecard, the framework becomes clear: Approximation error $\mathcal{E}_{\mathrm{app}}$ — Meaning: The model class cannot represent the relevant relationship; Typical remedy: Change the representation, functional form, or mechanism. Estimation error $\mathcal{E}_{\mathrm{est}}$ — Meaning: The available sample does not identify the model precisely; Typical remedy: Obtain better data, regularize, pool information, or redesign measurement. Optimization error $\mathcal{E}_{\mathrm{opt}}$ — Meaning: The algorithm does not reach an adequate solution; Typical remedy: Improve initialization, search, convergence checks, or optimization design. Numerical error $\mathcal{E}_{\mathrm{num}}$ — Meaning: Finite precision or approximation distorts the calculation; Typical remedy: Improve conditioning, precision, discretization, or numerical method. Distribution-shift error $\mathcal{E}_{\mathrm{shift}}$ — Meaning: The deployment environment differs from the training environment; Typical remedy: Reweight, adapt, stress-test, monitor, or restrict deployment.

This table also explains why model selection cannot be delegated entirely to a performance leaderboard. A more flexible model may reduce approximation error while increasing estimation error. More training may reduce optimization error but leave the underlying model misspecified. Higher numerical precision cannot repair a poor causal assumption. Additional data from the wrong population may even increase confidence in the wrong answer.

Competence in AI/data science begins with the ability to locate the dominant error rather than applying the same remedy to every failure.

Applied Case: Systemic Financial Risk

Systemic financial risk illustrates why the integration is necessary. Suppose $W_{ij}$ measures the exposure of institution $i$ to institution $j$, $s_i$ is an initial loss, and $h(\cdot)$ transforms a loss into financial distress. A simplified propagation model might take the form

where $\rho$ controls the intensity of transmission.

The object of interest may be a tail probability:

The formula is compact; the research problem is not. Direct observation of every bilateral exposure may be impossible. The network must be estimated or partially reconstructed. The distribution of initial shocks must be specified. The distress function $h$ may contain thresholds or nonlinear feedback. The system may have multiple equilibria. Each simulated scenario requires repeated propagation through the network.

A machine-learning procedure might estimate missing links in $W$. Econometrics might identify $\rho$ from historical variation. Numerical analysis determines whether the iteration is stable. Financial knowledge determines whether the distress mechanism is plausible. Simulation estimates $q_{\tau}$. Decision theory connects that estimate to capital requirements or intervention.

Calling this exercise “data analysis” understates the intellectual task. Calling it “software development” confuses implementation with validity. The output is a computational claim whose credibility depends on every layer of the system.

The same logic applies in computational biology, energy-system modelling, logistics, epidemiology, and language modelling. Different domains supply different mechanisms and evaluation standards. The common method is the disciplined conversion of assumptions and observations into computationally testable implications.

Implications for AI Education

If AI/data science is computational science, the curriculum cannot be organized as a catalogue of software tools. Tools change quickly; the intellectual structure changes more slowly.

Expressed as a practical comparison rather than another table, the distinctions are clear: Problem formulation — Central question: What is the object of inference or decision?; Required disciplines: Domain knowledge, economics, decision theory; Evidence of competence: A precise target and a defensible success criterion. Data-generating process — Central question: Why do these observations exist?; Required disciplines: Probability, statistics, econometrics; Evidence of competence: Identification of selection, measurement, dependence, and confounding. Mathematical representation — Central question: Which structure is retained or omitted?; Required disciplines: Linear algebra, calculus, probability, optimization; Evidence of competence: Explicit assumptions and interpretable model architecture. Computation — Central question: How is the answer approximated under constraints?; Required disciplines: Algorithms, numerical methods, computer science; Evidence of competence: Correct, efficient, and reproducible implementation. Validation — Central question: Under which conditions does the claim survive?; Required disciplines: Statistical inference, experimental design, stress testing; Evidence of competence: Out-of-sample tests, uncertainty analysis, and falsification attempts. Decision — Central question: What changes because the model exists?; Required disciplines: Utility, risk, institutional judgment; Evidence of competence: A decision rule with costs, benefits, and boundaries.

This curriculum does not require every student to become a specialist in every contributing discipline. It requires students to understand where each discipline enters the validity of the final claim.

An engineer who ignores sampling and identification may build a fast answer to the wrong question. A statistician who ignores algorithms and numerical constraints may specify an estimator that cannot be deployed. An economist who ignores representation learning may impose structure where the relevant pattern is too complex to specify manually. A software developer who ignores the data-generating process may reproduce code perfectly while reproducing a biased conclusion.

The educational objective is therefore not the accumulation of disconnected techniques. It is the formation of model judgment: the ability to trace a result backward from decision to computation, from computation to model, from model to assumptions, and from assumptions to the process that generated the data.

What Agentic AI Can Prove and What It Still Fabricates separates tasks with hard computational verification from open-ended judgments that remain difficult to validate. From Feedback Loops to Causal Guardrails shows why deployment changes the data-generating process itself, while research on organizational capability places computation inside a wider production and governance system. An AI result is therefore a joint claim about data, computation, uncertainty, and use.

Conclusion

AI/data science is often marketed as the ability to obtain value from data. That definition is too loose for advanced education. Data do not produce conclusions by themselves, and algorithms do not determine their own meaning.

A defensible result emerges from an integrated system:

Every arrow can fail. Every failure requires a different form of knowledge. Mathematics defines structure; statistics and econometrics connect that structure to observations; computer science and numerical methods make the calculation feasible; domain disciplines determine whether the representation is credible; decision theory determines whether the result is useful.

This is why SIAI GSB treats AI/data science as computational science. The purpose of education is not to train students to operate the latest software package. It is to train them to construct, calculate, question, and defend model-based claims about complex systems.

References

Leo Breiman, “Statistical Modeling: The Two Cultures”, Statistical Science 16, no. 3 (2001): 199–231.
David Donoho, “50 Years of Data Science”, Journal of Computational and Graphical Statistics 26, no. 4 (2017): 745–766.
Roger D. Peng, “Reproducible Research in Computational Science”, Science 334, no. 6060 (2011): 1226–1227.
Galit Shmueli, “To Explain or to Predict?”, Statistical Science 25, no. 3 (2010): 289–310.
SIAM Working Group on CSE Education, “Graduate Education in Computational Science and Engineering”, SIAM Review 43, no. 1 (2001): 163–177.
Swiss Institute of Artificial Intelligence (2026) ‘What Agentic AI Can Prove and What It Still Fabricates: The Real Frontier of Machine Science’, SIAI Science Review, 15 August.
Swiss Institute of Artificial Intelligence (2026) ‘From Feedback Loops to Causal Guardrails: Endogeneity in AI Systems’, SIAI AI Memo, 20 June.
Swiss Institute of Artificial Intelligence (2026) ‘From AI Access to Organizational Capability: Pricing the Corporate AI Transition’, SIAI Working Papers, 9 August.