Data-driven surrogate models are increasingly used to simulate continuous dynamical systems, offering an efficient alternative to traditional methods. However, autoregressive rollouts of these models often suffer from instability and spectral blow-up.

JAWS: An Innovative Solution

The new approach, called JAWS (Jacobian-Adaptive Weighting for Stability), addresses these limitations through a probabilistic regularization strategy. JAWS dynamically modulates the regularization strength based on local physical complexity, allowing the model to enforce contraction in smooth regions to suppress noise, and relaxing constraints near singular features to preserve gradients. This behavior is similar to numerical shock-capturing schemes.

Benefits and Performance

Experiments on the 1D viscous Burgers' equation demonstrate that JAWS serves as an effective spectral pre-conditioner, reducing the base operator's burden of handling high-frequency instabilities. This enables memory-efficient, short-horizon trajectory optimization that matches or exceeds the long-term accuracy of long-horizon baselines. The hybrid approach improves long-term stability, shock fidelity, and out-of-distribution generalization while reducing training computational costs.

For those evaluating on-premise deployments, there are trade-offs to consider. AI-RADAR offers analytical frameworks on /llm-onpremise to evaluate these aspects.