Learning Implicit Solves for Dynamic Simulations

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.

动力系统的保真模拟对于科学发现和工程设计至关重要，但其计算需求依然巨大。在此，我们引入了隐式神经算子求解器（INOS），它能够学习隐式求解并编码时间积分器。

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.

INOS 通过静态平衡解预训练神经算子，并将其重用于 Newmark-$\beta$ 积分中。在每个时间增量中，积分器会形成一个有效的平衡问题，预训练的神经算子推断出下一步的解场，随后 Newmark 关系式推进动态状态。

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.

在线性和非线性弹性动力学的数值算例中，该方法在没有动态轨迹监督的情况下展示了精确的全场预测。对比结果表明，INOS 在零样本评估下，比在动态模拟上训练的神经求解器基准具有更高的预测精度。

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.

此外，与顺序经典有限元求解器相比，INOS 在非线性模拟中实现了超过 4,600 倍的加速。INOS 原生地适应动态条件的变化，并支持在空间和时间离散化中重用预训练算子。进一步的评估证明了其百万步展开的稳定性。