Physics-consistent AI simulation realized with mesh field theory

A research group including Researcher Satoshi Noguchi at the Center for Mathematical Science and Advanced Technology, Research Institute for Earth and Information Sciences, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), proposed "Mesh Field Theory (MeshFT)," a theory for simulating physical phenomena using machine learning. It is expected to contribute broadly to the understanding and prediction of natural phenomena. The results were accepted and presented at "ICML 2026," a top conference in the field of machine learning held in South Korea from July 6 to 11.

Physical simulation is a foundational technology for understanding physical phenomena such as fluids, solids, and electromagnetism. Numerical analysis of physical phenomena is often performed using a "mesh" that divides space into a grid.

In recent years, because such analyses require vast amounts of computational resources, the realization of analysis using machine learning and AI for speedup and other purposes has been highly anticipated. On the other hand, a major challenge in applying AI is that the flexibility, which is an advantage of AI, offers no guarantee of consistency with physical laws. While various approaches are being discussed, many embed governing equations as known priors, making them difficult to apply to unknown systems.

Based on the principle of determining what AI should and should not learn, the research group devised a method to separate the universal structure of physical phenomena that does not depend on specific phenomena from the structure that should be estimated from data. They aimed to overcome the challenge by theoretically fixing the structure universal to physical phenomena and estimating only the latter using AI.

Specifically, they incorporated the following four principles as universal concepts:

1. (L) Locality: Physical phenomena correlate only nearby, and phenomena do not instantaneously propagate far away.
2. (P) Permutation equivariance: Symmetry of labeling.
3. (O) Orientation consistency: Universality of orientation choice.
4. (E) Energy: Prohibiting unnatural energy increases.

As a result, they were able to mathematically prove that general physical phenomena on a mesh satisfying these principles are locally reduced to a port-Hamiltonian form. Furthermore, in numerical experiments implementing the theory as a machine learning model, they confirmed that the accuracy was one to two orders of magnitude higher than conventional models, high learning efficiency was obtained with less data, and high consistency with physical laws was achieved.

Noguchi commented "I believe this achievement will contribute to stable and highly reliable predictions even from sparse observational data, and lead to the establishment of a new scientific computing platform integrating physics and data science that contributes to the understanding and prediction of ocean, Earth, and life systems. Moving forward, we intend to verify whether it can be applied to actual simulations such as weather science, while also aiming for expansion into quantum physics."