Learning missing physics from legacy simulators with alternating neural integrators.

Area of Science:

• Computational Science and Engineering
• Scientific Machine Learning
• Numerical Analysis

Background:

• The model-reality gap challenges scientific and engineering simulations, stemming from unresolved physics or incomplete models.
• Existing solutions include imperfect mechanistic models or fully data-driven surrogates, each with limitations.
• Legacy simulators often lack fidelity due to these inherent gaps.

Purpose of the Study:

• To introduce Alternating Neural Integrators (ANI), a novel framework for enhancing legacy simulators.
• To provide a non-intrusive method for upgrading simulator fidelity without modifying internal code.
• To address the model-reality gap by integrating data-driven corrections with existing simulation infrastructure.

Main Methods:

• ANI employs an operator-splitting approach, alternating between a fixed legacy simulator and a learned neural correction.
• The neural network is trained to identify and correct discrepancies between the simulator's predictions and supervisory data.
• This framework operates as a gray-box method, requiring only a callable simulator and supervisory data.

Main Results:

• ANI successfully recovers missing coupling in chaotic systems, enhancing dynamical fidelity.
• The framework acts as an effective subgrid correction in turbulence simulations, mitigating model drift.
• Symbolic distillation of learned corrections yields interpretable hypotheses and supports refinement of prior models.

Conclusions:

• Alternating Neural Integrators offer a practical and theoretically grounded approach to systematically upgrade computational infrastructure.
• ANI combines the flexibility of data-driven methods with the reusability of scientific simulators.
• This work presents a viable gray-box strategy for improving the accuracy and reliability of existing simulation tools.