The paper introduces the Latent Generative Solver (LGS), a neural PDE solver that combines a Physics VAE, a Pyramidal Flow-Forcing Transformer, and input noising to achieve generalization across twelve PDE families and stable long-term rollouts. LGS matches or surpasses deterministic baselines on one-step predictions, outperforms them on 5- and 10-step rollouts, and significantly reduces long-horizon error while cutting compute costs. It also adapts efficiently to unseen higher-resolution systems, demonstrating strong empirical performance on 2D regular-grid PDE simulations.
arXiv:2608. 00675v1 Announce Type: cross Abstract: Autoregressive models accumulate error over long rollouts, yet at deployment there is no ground truth to measure it against.
arXiv:2605. 08318v2 Announce Type: replace Abstract: We study the problem of \emph{architecture selection} for deep learning models trained to solve partial differential equations (PDEs), asking when transformer-based architectures with learned attention outperform Fourier-domain neural operators.
arXiv:2607. 21644v1 Announce Type: new Abstract: We present a goal-agnostic control framework for partial differential equations (PDEs) built around a joint-embedding predictive architecture (JEPA).
arXiv:2604. 18194v2 Announce Type: replace Abstract: Single-step generators promise high-fidelity synthesis at a fraction of the inference and training cost of ordinary differential equation (ODE)-based flow models, a central concern when compute is limited.
The paper introduces Untied Self-Conditioning, a sampler that corrects a train–inference mismatch in flow‑matching language models. By dampening redundant directions in the self‑conditioning input and approximating a step‑average prediction from history, the method improves generation quality without retraining. On LangFlow and ELF‑B datasets, it dramatically lowers perplexity and is preferred in the majority of pairwise comparisons.
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
arXiv:2608. 11937v1 Announce Type: new Abstract: 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.
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
The paper introduces the first controlled benchmark for optimizers in discrete diffusion models, evaluating seven optimizers (AdamW, Lion, Muon, SOAP, MARS, MARS‑M, Schedule‑Free) across four diffusion formulations: masked diffusion on text8, uniform diffusion on QM9 and LM1B, and Gaussian diffusion on CelebA‑64. Each optimizer undergoes the same search protocol and is retrained with full budget and multiple seeds, revealing that AdamW, while strong, is not universally optimal and that optimizers validated on autoregressive language models (Muon, MARS‑M, SOAP) can outperform tuned AdamW on certain tasks.
arXiv:2607. 04113v1 Announce Type: new Abstract: Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $\sigma_{\min}$, at which the score is stiff and the flow develops a boundary layer.
The paper introduces a new type of data‑poisoning attack called a wrong‑physics backdoor, which tricks neural PDE operators into selecting a solution from the same PDE family but with an incorrect physical parameter. By relinking a surrogate input’s supervision to a cached alternate‑parameter solution, the attack keeps the output physically plausible yet wrong for the intended parameter. Experiments on 476 campaigns across several PDEs and models (FNO, DeepONet, Transformer, GRU, LSTM) show high success rates while maintaining low clean error, revealing a validation gap in current practices.
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.