arXiv AI
Jun 10
Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.
PI-JEPA: Label-Free Surrogate Pretraining for Coupled Multiphysics Simulation via Operator-Split Latent Prediction
arXiv:2604. 01349v4 Announce Type: replace Abstract: Reservoir simulation workflows face a fundamental data asymmetry: input parameter fields (geostatistical permeability realizations, porosity distributions) are free to generate in arbitrary quantities, yet existing neural operator surrogates require large corpora of expensive labeled simulation trajectories and cannot exploit this unlabeled structure.
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arXiv Machine Learning
Sep 25
Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solvers
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 Machine Learning
Aug 7
Kastor: An efficient fine-tuning strategy for generative emulation of PDE simulations
arXiv:2608. 06107v1 Announce Type: new Abstract: Machine learning offers a promising avenue to accelerate physical simulations by replacing computationally expensive traditional Partial Differential Equation (PDE) solvers with fast, differentiable surrogate models.
arXiv Machine Learning
Aug 14
Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv Machine Learning
Jun 5
On the training of physics-informed neural operators for solving parametric partial differential equations
arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.
arXiv Machine Learning
Sep 7
Disentangling Attention in Deep Operator Learning: A Controlled Study of Data-Driven and Physics-Informed Architectures
The paper investigates how different attention mechanisms affect the performance of DeepONet neural operators. Five variants—varying in cross‑attention, self‑attention, tokenization, and attention depth—are trained in both data‑driven and physics‑informed settings on one‑ and two‑dimensional PDE benchmarks. Results show that per‑sensor tokenization with cross‑attention consistently reduces error, while branch self‑attention helps only in complex spatial problems, and deeper cross‑attention yields diminishing returns with higher cost.
arXiv Machine Learning
Jun 17
Operator Boosting Produces Pareto-Efficient PDE Surrogates
arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.
Hugging Face Trending Papers
Jun 4
On the training of physics-informed neural operators for solving parametric partial differential equations
Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.
arXiv AI
4d ago
Transolver-$\sigma$: Joint Spectral-Physical Subspace Modeling for Neural PDE Solving
Transolver‑σ is a neural PDE solver that jointly models spectral and physical subspaces to improve accuracy in both one‑step and autoregressive rollouts. The method uses adaptive physical-state interactions, Slice‑Residual Physics‑Attention, and an axis‑factorized Fourier operator to enable information exchange between representations. Across five standard PDE benchmarks, Transolver‑σ reduces benchmark‑averaged relative error by 33.4% compared to the strongest baseline and shows strong performance on coupled multiphysics systems and real‑world fluid and combustion data.
arXiv AI
Jun 26
Error-Conditioned Neural Solvers
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.
arXiv Machine Learning
Jun 16
Pre-Training for Simulation-Based Science: A Study on Jet Foundation Model Training Objectives
arXiv:2606. 14870v1 Announce Type: cross Abstract: Foundation models (FMs) trained on large datasets and fine-tuned on downstream tasks have emerged as a powerful paradigm in AI for science.
arXiv AI
6d ago
Latent Generative Solvers for Generalizable Long-Term Physics Simulation
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.