Fundamental AI/ML design and reliability questions for physics-based applications

Determine appropriate neural network architectures (including depth and width), quantify sufficient training data requirements, develop training approaches for highly nonconvex optimization problems, establish accuracy guarantees, and identify conditions under which Artificial Intelligence/Machine Learning methods can be trusted when applied to physics-based problems lacking explicit physics models.

Background

The report highlights that purely data-driven AI/ML approaches can fail to generalize on basic physics-based models, underscoring the need for mathematical rigor to understand and improve their performance in scientific and engineering contexts.

Within this discussion, the authors explicitly note that several foundational aspects of AI/ML—such as model architecture selection, data sufficiency, training strategies for nonconvex problems, accuracy expectations, and trustworthiness—remain unresolved, especially for physics problems formulated without explicit governing laws.

References

Additionally, most of the fundamental questions remain open, for instance, what kind of network should be used, the size (depth and width) of the network, how much training data is sufficient, how to train highly nonconvex optimization problems, what to expect in terms of accuracy and when one can trust these approaches. In many cases it is not even clear how to rigorously phrase these questions, especially for physics problems `in the absence of physics'.

— Mathematical Opportunities in Digital Twins (MATH-DT)  (2402.10326 - Antil, 2024) in Subsection “Background” (Section 2.1)

These findings raise broader questions: To what extent and how much physical consistency should machine learning weather forecasting models adhere to, acknowledging that these are not built as general purpose fluid dynamics solvers but only for the purpose of weather forecasting? To what extent does an inaccurate representation of known energy transfer across spatial scales undermine the trustworthiness of these models, given that their forecasts may nevertheless be judged to be of high quality according to other metrics?

— Butterfly Effect and the Kinetic Energy Cascade in Probabilistic Machine Learning Weather Prediction Models  (2609.18489 - Chen et al., 16 Sep 2026) in Section 5, “Conclusions”

The main challenge is no longer simply whether neural networks can fit holographic data, but whether the reconstructed bulk structures are unique, physically interpretable, and predictive outside the training regime.

— Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery  (2610.12293 - Chen et al., 8 Oct 2026) in Section 6, 'Short Summary and Outlook'

Can AI reduce the cost of first-principles or high-fidelity calculations without compromising exactness or controlled uncertainty? This is the central question for lattice samplers, hydrodynamic emulators, and differentiable solvers.

— Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery  (2610.12293 - Chen et al., 8 Oct 2026) in Section 11, Conclusions and outlook

Can AI improve the information extracted from existing and future data? This is the central question for heavy-ion event-level learning, neutron-star simulation-based inference, and optimized observables for criticality or CME searches.

— Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery  (2610.12293 - Chen et al., 8 Oct 2026) in Section 11, Conclusions and outlook

Several directions remain open. These include connecting empirical distributional training more directly to the approximation theory, understanding long-time behavior and Chapman--Kolmogorov consistency, developing more expressive non-Gaussian transition models, and extending physics conformity beyond conserved quantities to dissipative structure. Scalable architectures for high-dimensional stochastic systems are another important direction.

— Stochastic Latent Twins: Learning Stochastic Solution Operators  (2610.21084 - Chung et al., 15 Oct 2026) in Section Conclusion and outlook

Open questions include how many lifted channels and which architecture a problem requires, how the lift converges as it grows, and how far the idea extends to chaotic turbulent flows, which are closer to real applications.

— SALTO: Solver-Anchored Lifted Transfer Operators for Nonlinear Event Inference  (2610.21049 - Wang et al., 15 Oct 2026) in Section 6, Discussion and Outlook