Discovering Thermodynamically Admissible Dissipation Potentials via Grammar-Based Symbolic Regression
Researchers have developed a symbolic regression framework that discovers interpretable equations for material behavior while guaranteeing thermodynamic consistency, a long-standing tension in physics-informed machine learning. By embedding Clausius-Duhem inequality constraints directly into grammar-based symbolic search, the work bridges data-driven discovery and formal physical law, addressing a critical gap where neural networks often learn physically plausible but opaque models. This approach matters for materials science, engineering simulation, and the broader push toward AI systems that satisfy hard physical constraints rather than merely approximating them, signaling maturation in how ML handles domains where interpretability and correctness are non-negotiable.
Modelwire context
ExplainerThe paper's actual novelty is narrower than it sounds: symbolic regression itself isn't new, but enforcing thermodynamic validity during search (not post-hoc filtering) is. The constraint lives inside the grammar, not bolted on afterward.
This work sits in direct conversation with the surrogate modeling failure modes identified in 'The Dynamic-Probabilistic Consistency Gap' from late May. Both papers diagnose the same core problem: standard ML objectives can learn models that look plausible but violate the physics they're supposed to capture. Where that paper showed how probabilistic accuracy can corrupt learned dynamics, this one proposes a preventive architecture that bakes physical law into the search space itself. The difference is philosophical: one identifies what breaks, the other prevents the break from happening. Both suggest that for scientific computing, the training objective alone is insufficient.
If this grammar-based approach produces dissipation potentials that outperform both unconstrained symbolic regression and physics-informed neural networks on held-out material datasets within the next 12 months, it signals that constraint-embedding is genuinely superior to post-hoc validation. If instead the gains vanish on materials outside the training regime, the method may only work for interpolation, not discovery.
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MentionsGeneralized Standard Materials (GSM) · Clausius-Duhem inequality · symbolic regression · grammar-based search
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