Learning Implicit Solves for Dynamic Simulations

A new arXiv paper (2611.05439v1) introduces the Implicit Neural Operator Solver (INOS), which learns the implicit solve in dynamical simulations by pretraining a neural operator on static equilibrium solutions and reusing it inside Newmark-β time integration. In linear and nonlinear elastodynamics tests, INOS evaluated zero-shot predicted full fields more accurately than neural solver baselines trained on dynamic simulations, and delivered over 4,600× speedup in nonlinear simulations versus sequential classical finite-element solvers. The authors report a stable million-step rollout and reuse of the pretrained operator across spatial and temporal discretizations, positioning INOS as a reusable neural implicit solver for dynamic modeling.

arXiv:2611.05439v1 Announce Type: new Abstract: High-fidelity simulation of dynamical systems is central to scientific discovery and engineering design, yet remains computationally demanding. Here we introduce the Implicit Neural Operator Solver INOS , which learns the implicit solve and encodes a time integrator. INOS pretrains a neural operator from static equilibrium solutions and reuses it within Newmark-$\beta$ integration. At each time increment, the integrator forms an effective equilibrium problem, the pretrained neural operator infers the next-step solution field, and the Newmark relations advance the dynamic state. Numerical examples in linear and nonlinear elastodynamics demonstrate accurate full-field predictions without dynamic trajectory supervision. Comparative results show that INOS, evaluated zero-shot, achieves higher predictive accuracy than neural solver baselines trained on dynamic simulations. In addition, INOS delivers over 4,600$\times$ speedup in nonlinear simulations over sequential classical finite-element solvers. INOS natively accommodates changes in dynamic conditions and enables reuse of the pretrained operator across spatial and temporal discretizations. Further evaluation demonstrates a stable million-step rollout. These findings establish INOS as a reusable neural implicit solver for accurate, efficient, and robust dynamic modeling.