Identify governing equations for domains with unknown physics

Ascertain which partial differential equations or ordinary differential equations correctly describe the basic physics in application domains—such as engineering, biology, medicine, and materials science—where the underlying physics is still unknown.

Background

The authors emphasize that in many domains relevant to digital twins, the fundamental physical laws remain undetermined, posing a barrier to reliable modeling and simulation.

They note that until the appropriate governing equations are identified, mathematical analysis, validation, and downstream tasks such as reduced-order modeling and uncertainty quantification cannot be systematically developed for these systems.

References

In many areas of engineering, biology, medicine and material science the basic physics of the problem are still unknown. This implies that at this point we do not know which are the relevant PDEs or ODEs that properly describe the physics.

— Mathematical Opportunities in Digital Twins (MATH-DT)  (2402.10326 - Antil, 2024) in Subsection “Summary of Challenges” (Section 6.1), bullet “Gaps In Forward Problems”

Scope: the meter here uses the known interaction law $V(q;G)$; on real video, selecting the form that becomes the meter is an open form-selection problem.

— Conservation Buys Stability and Factoring Buys Counterfactuals in Physical World Models  (2609.19674 - Wang et al., 17 Sep 2026) in Appendix H, subsection “A grounded energy-balance estimator”