AI Agents Discover Physics-Law-Abiding Material Models, Bridging Simulation and Reality

In a breakthrough that could redefine how engineers design everything from car tires to artificial arteries, researchers have developed an AI framework that autonomously discovers material laws that not only fit experimental data but also strictly obey the fundamental laws of physics. The new system, dubbed Engineering-Oriented Symbolic Regression (EO-SR), leverages large language models as 'physics-informed agents' to bridge a critical gap that has long plagued computational mechanics: the divide between data-driven accuracy and numerical robustness in simulation. This approach marks a significant departure from traditional s, where models optimized solely for fitting error often fail catastrophically when implemented in finite element analysis software, leading to non-convergence and unreliable predictions.

At the heart of the innovation is a modular architecture where an LLM agent—specifically Gemini3-pro—acts as a domain expert, translating high-level physical concepts into executable mathematical constraints. Unlike standard symbolic regression, which functions as an unconstrained mathematical search engine prone to generating 'physically invalid' expressions, the EO-SR framework injects these constraints directly into process. For hyperelastic materials like rubber, the agent automatically synthesizes requirements such as thermodynamic consistency (Drucker stability) and frame indifference, ensuring that any discovered constitutive law maintains unconditional convexity. This transforms symbolic regression from a mere curve-fitting exercise into a physics-governed engine, capable of producing models that are both empirically accurate and simulation-ready.

The framework's efficacy was rigorously validated using the classic Treloar dataset for rubber-like materials, a gold standard in the field. Operating solely on standard uniaxial and biaxial tensile data—avoiding the need for expensive full-field measurements—the system discovered a novel hybrid constitutive law. This model combines a Mooney-Rivlin linear base with a rational locking term, expressed as W = 0.031(3.75Ĩ₁ + Ĩ₂) + Ĩ₁/(77.9 - 1.05Ĩ₁), where Ĩ₁ and Ĩ₂ are shifted invariants. Remarkably, this model achieved high predictive accuracy across multiple deformation modes, including a zero-shot prediction of pure shear with an MSE of approximately 0.0048, outperforming industry-standard models like Yeoh and Ogden in generalization capability.

Perhaps most impressively, the discovered model demonstrated unparalleled numerical robustness in finite element simulations. When implemented in Abaqus/Standard for a complex double-edge notched tensile specimen—a scenario where tension, shear, and transverse compression coexist—the model maintained smooth convergence even under severe distortion. In stark contrast, an Ogden model (N=3), optimized purely for fitting error, failed to converge due to a hidden mathematical singularity triggered by transverse compression. This failure was traced to a large negative exponent in the Ogden parameters, causing a stiffness component to explode exponentially as compression increased, ill-conditioning the Jacobian matrix and halting the solver.

Of this work extend far beyond hyperelasticity. The modular 'skill' architecture of the EO-SR framework is designed for generalization to other complex systems, such as fiber-reinforced soft tissues or fluid dynamics. In a conceptual case study on arterial walls, the framework demonstrated its ability to enforce logical branching constraints—like tension-compression asymmetry, where fibers stiffen under tension but buckle under compression—guiding toward structurally valid models akin to the Holzapfel-Gasser-Ogden prototype. This highlights the framework's role as a semantic compiler, capable of translating abstract physical logic into constraints that purely numerical s cannot grasp.

However, the approach is not without limitations. While the symbolic regression engine itself is efficient, the 'skill injection' and 'agent-assisted selection' phases incur latency due to LLM inference, though the architecture strategically places the agent outside the evolutionary loop to minimize cost. Additionally, extending the framework to anisotropic materials will require planar biaxial testing data to decouple matrix and fiber properties, though this remains within the realm of standard, accessible equipment rather than high-barrier optical setups. Future work will focus on instantiating 'plasticity skills' for yield surfaces and further optimizing agent efficiency through domain-distilled checkpoints.

Ultimately, this research establishes a new paradigm for 'AI for Science,' where foundation models serve not merely as coding assistants but as guardians of theoretical consistency. By enforcing fundamental axioms like frame indifference and thermodynamic stability, the EO-SR framework elevates AI-discovered models from empirical regressions to mathematically rigorous constitutive closures. This bridges the long-standing divide between data-driven description and predictive physical realism, offering a low-barrier pathway to simulation-ready models that could accelerate innovation in materials science, biomedical engineering, and beyond. Reference: Wu et al., 2026, arXiv:2603.19241.