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Life sciences · Preprint
arXiv · August 12, 2026
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This unreviewed preprint proposes TREX, a knowledge distillation framework to compress foundation models for time-dependent PDEs into faster, smaller student models by generating synthetic training trajectories from a fine-tuned teacher. Reported results claim parameter reduction by orders of magnitude and speedup greater than 10× while maintaining or improving accuracy, but the work has not undergone peer review and lacks independent validation.
Method development with computational experiments. Time-dependent PDEs from diverse physical systems; fine-tuned on few trajectories from target domains.. Intervention: Teacher Rollout Extension (TREX) knowledge distillation framework with synthetic trajectory generation and periodic noise injection.. Compared with: Pretrained (non-distilled) foundation model teacher.
Student models achieved parameter reduction by several orders of magnitude relative to teacher Inference speedup of more than an order of magnitude (>10×) reported Students matched or surpassed teacher accuracy on multiple PDE benchmarks
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This is an unreviewed preprint presenting a novel knowledge distillation method for PDE models with computational results on benchmarks, but lacks peer review, clinical or real-world validation, and independent replication.
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Foundation models for time-dependent partial differential equations (PDEs) are trained on large and diverse collections of physical systems and can generalize effectively to new downstream tasks. After fine-tuning on only a few trajectories from a target domain, they can achieve strong accuracy in low-data regimes. However, these models are typically large and computationally intensive, limiting their usefulness as fast surrogates for numerical solvers. We propose Teacher Rollout Extension (TREX), a knowledge distillation framework that transfers the predictive capability of a pretrained foundation model into a compact and efficient student. Starting from a fine-tuned teacher, TREX augments limited downstream data by generating long synthetic trajectories through teacher rollouts, optionally with periodic noise injection. This procedure samples from the teacher-induced rollout distribution without requiring explicit knowledge of the initial-condition distribution, while exposing the student to long-horizon states and local recovery behavior around states encountered during autoregressive prediction. The student can further incorporate task-specific inductive biases, such as equivariance, that the teacher does not necessarily enforce. We evaluate TREX on multiple PDE benchmarks. The resulting students can match or surpass the teacher's accuracy while reducing the number of parameters by several orders of magnitude and achieving more than an order-of-magnitude speedup in inference.
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