Architecture Optimization to Stabilize and Accelerate Latent Neural Solvers for Mesoscale Materials Modeling
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Neural network based partial differential equation solvers have emerged as an alternative solver strategy ideal for applications demanding high volume calculations, such as inverse design and uncertainty propagation. Their design must achieve high solver speeds – their premier characteristic – while maintaining sufficient accuracy and low development cost (e.g., low data curation and training costs). Unfortunately, these are often in direct opposition. In this talk, we analyze the sources of instability and high computational cost in current operator frameworks. In particular, we study the instabilities present in latent space methods – methods that perform compression before modeling evolution. We present a series of improvements, including architectural adaptations and incorporating physics/control based inductive biases, that significantly improve the stability and performance of latent space methods. These improvements enable both high solver speeds and low errors. We demonstrate the impact of these improvements on a series of salient problems in solid mechanics and mechanics of materials, including crystal plasticity based cyclic fatigue and spinodal decomposition. Mandatory disclaimer: SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. SAND No. SAND2026-15905A.
