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The paper introduces the Retain-and-Repair Neural Operator (R$^2$NO), a method that adapts neural operators pretrained on numerical simulations to real-world data while preserving useful pretrained structure. R$^2$NO first fine‑tunes the pretrained operator on real data, freezes it to serve as a source prediction, and then employs a shared repair module that learns refinements via orthogonal Fourier projections and a spectral ensemble of ridge regressions. The approach allows refinement depth to vary across frequency magnitude, orientation, and channels, and consistently outperforms full fine‑tuning and iterative refinement on RealPDEBench systems across six backbones.
arXiv:2606. 16602v1 Announce Type: new Abstract: Neural operator models trained on simulation data often lose accuracy when applied to experimental measurements due to the sim-to-real gap.
The paper investigates why latent neural surrogate solvers, which compress physical system dynamics into a lower‑dimensional space, often fail during long‑horizon autoregressive rollouts. It demonstrates that training the latent representation only for reconstruction leads to instability, and proposes a set of training interventions—Koopman operator learning, Hamming noise injection, and multi‑step rollout fine‑tuning—that align the latent space with long‑horizon forecasting. These interventions reduce long‑rollout error by about 40 % and achieve accuracy comparable to full‑resolution models while using far fewer floating‑point operations and GPU memory, enabling stable extrapolation in mesoscale crystal‑plasticity simulations of high‑cycle fatigue.
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
The paper introduces an in‑span adaptation technique for reduced‑order models, where the reduced subspace is continually updated using the model’s own predictions via an incremental singular‑value decomposition with a forgetting factor. This creates a trajectory‑informed spectral preconditioner that reweights and realigns the basis without changing the subspace, enabling the model to better absorb future out‑of‑span corrections. The authors demonstrate the method on a 3‑D spiral example and nonlinear PDEs such as viscous Burgers and Fisher–KPP, and relate the approach to in‑context learning in dynamical systems.
SPARCL introduces a spectral partitioned analytic continual learning method that addresses forgetting in analytic class‑incremental learning. By decomposing the running autocorrelation into a high‑energy core and a residual complement, SPARCL freezes core components for old classes and updates only the residual block, ensuring closed‑form updates with an invariance guarantee. Experiments on CIFAR‑100, CUB‑200, ImageNet‑R, and ImageNet‑A with a frozen ViT‑B/16 protocol show that SPARCL narrows the performance gap between classical analytic learners and strong representation matchers while complementing sparse feature‑decorrelation approaches.