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Learning Physically Consistent Dynamics: A Human-Centric Approach to Entropy-Stable Neural Networks
Issue Vol. 1 No. 01 (2024): VOLUME01 ISSUE01 --- Section Articles
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Abstract
From the flow of galaxies to the waves in our oceans, much of the physical world is governed by a class of equations known as hyperbolic conservation laws. Simulating these laws on computers is a monumental task, especially because they often produce sharp, sudden changes like shockwaves. For decades, scientists have hand-crafted complex numerical methods to tackle this challenge, but these methods require deep, specialized knowledge. More recently, artificial intelligence has shown an incredible ability to learn dynamics from data, but these "black-box" models often fail to respect the fundamental laws of physics, leading to unstable or nonsensical results.
In this paper, we introduce a new approach that bridges this gap: the Neural Entropy-Stable Conservative Flux (NES-CF) network. Instead of relying on predefined rules, our framework learns the physics of a system directly from data. Our key innovation is to have the AI learn not only the system's dynamics but also a fundamental physical principle known as entropy—a measure of disorder that must always be respected. By building this principle directly into the learning process, our model guarantees that its predictions are physically consistent and stable. We tested our framework on a range of challenging problems, from the simple formation of a shockwave to the complex dynamics of gas, and found that it accurately captures the physics, even when trained with noisy data. This work represents a significant step toward creating AI models for science that are not only powerful but also trustworthy..
