A new family of Constitutive Artificial Neural Networks towards automated model discovery

For more than 100 years, chemical, physical, and material scientists have proposed competing constitutive models to best characterize the behavior of natural man-made materials in response mechanical loading. Now, computer science offers a universal solution: Neural Networks. Networks are powerful function approximators that can learn relations from large data without any knowledge underlying physics. However, classical ignore century research modeling, violate thermodynamic considerations, fail predict outside training regime. Here we design new family Constitutive Artificial inherently satisfy common kinematic, thermodynamic, physic constraints and, at same time, constrain space admissible functions create robust approximators, even presence sparse data. We revisit non-linear field theories mechanics reverse-engineer network input account for objectivity, symmetry, incompressibility; output enforce consistency; activation implement physically reasonable restrictions; architecture ensure polyconvexity. demonstrate this class is generalization neo Hooke, Blatz Ko, Mooney Rivlin, Yeoh, Demiray weights clear physical interpretation. When trained with benchmark rubber, our autonomously selects model learns its parameters. Our findings suggests potential induce paradigm shift user-defined selection automated discovery. source code, data, examples available https://github.com/LivingMatterLab/CANN.