arXiv AI
Jun 19
Bi-Anchor Interpolation Solver for Accelerating Generative Modeling
arXiv:2601. 21542v3 Announce Type: replace-cross Abstract: Flow Matching (FM) models have emerged as a leading paradigm for high-fidelity synthesis.
Holomorphic Cauchy Networks for Efficient Stationary Tail Computation in High-Dimensional Reflected Brownian Motions
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arXiv AI
Aug 24
STCO: Conditional Neural Operators for Time-Dependent PDEs
The paper introduces the Spatiotemporal Conditional Operator (STCO), a framework for learning neural operators that can incorporate prescribed target‑time condition fields—such as body motion, inflow disturbances, or body‑force actuation—into time‑dependent PDE simulations. STCO combines a Flow‑Aware Graph Leaf (FAGL) partitioning scheme with Dual‑Site Feature‑wise Linear Modulation (DSFiLM) to inject these conditions before and after the core operator computation. Evaluated on twelve backbone architectures across an immersed‑boundary CFD benchmark, STCO achieves significant reductions in relative‑L2 field error (31.1%) and pressure‑derived load error (24.7%) while improving long‑lead predictions for most backbones.
arXiv Machine Learning
Jul 24
FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers
arXiv:2607. 18020v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
arXiv Machine Learning
Jun 3
Scalable Derivative Gaussian Processes via Exact Gradient Reduction
arXiv:2606. 02909v1 Announce Type: cross Abstract: Gradient observations can substantially improve Gaussian process (GP) surrogates, particularly in high-dimensional settings where function evaluations are expensive.
arXiv Machine Learning
Jul 21
FlashPDE: A Drop-in Fused Triton Operator Library for Neural PDE Solvers
arXiv:2607. 18020v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
arXiv Machine Learning
Jul 21
Stochastic Dimension Zeroth-Order Estimator: Stable and Memory-Efficient Training of PINNs
arXiv:2603. 24002v3 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) for high-dimensional and high-order partial differential equations (PDEs) are primarily constrained by the $\mathcal{O}(d^k)$ spatial derivative complexity and the $\mathcal{O}(P)$ memory overhead of backpropagation (BP).
arXiv Machine Learning
Jun 11
HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems
arXiv:2606. 11963v1 Announce Type: new Abstract: Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space.
arXiv Machine Learning
2d ago
Self-Supervised Learning of Universal Latent Spaces for Operator Learning
arXiv:2611.05735v1 Announce Type: new Abstract: Neural operators fit their representation of functions to the task they are trained on, so every new task rebuilds a reduced space from labeled data. F...
arXiv Machine Learning
Sep 14
Physics-enriched neural solvers for transient ice-flow simulation
Physics-enriched neural solvers for transient ice-flow simulation present a method where a neural network represents the glacier velocity field, warm-started from the previous time step and updated with few optimizer iterations. By feeding the network inexpensive input fields derived from low-order ice-flow balances, the solver improves robustness and accuracy across three real-world glacier configurations, achieving surface-velocity errors reduced by factors of two to four at fixed runtime. The approach enables a 300-year Aletsch simulation to finish in under one minute on a single GPU, demonstrating significant computational savings compared to traditional higher-order models.
arXiv AI
Oct 21
Learning Computational Structure for Sample-Efficient Prediction
arXiv:2610.28555v1 Announce Type: cross Abstract: Statistical learning in high dimensions suffers from the curse of dimensionality. Fortunately, many functions of practical interest are compositional...
arXiv Machine Learning
Oct 16
The importance of tensor handling and implementation of physics-informed DeepONets
The paper presents a modified physics-informed DeepONet (PI-DeepONet) architecture that reduces computational cost by eliminating redundancy in the Branch network’s handling of input functions across collocation points. The new formulation is mathematically equivalent to the original but uses smaller input tensors and fewer network evaluations, leading to faster training while maintaining comparable predictive accuracy on 1D, 2D, and 3D linear advection problems. Experiments show up to a 3.75× speed‑up in 2D and enable feasible training of 3D models on an NVIDIA A100 GPU, where the original architecture fails due to memory limits.
arXiv Machine Learning
Oct 16
PotentialEP: Backprop-Free Training of CIFAR-Scale Generative Models via Equilibrium Propagation
The paper introduces PotentialEP, a backpropagation‑free method for training generative models at CIFAR scale using Equilibrium Propagation. It shows that a predictive coding network with a small linear injection can relax to a state that inherently carries the gradient needed for sampling, allowing an Energy Matching model trained with backpropagation to be sampled by relaxation alone with negligible loss in FID. Moreover, the authors demonstrate that training end‑to‑end with Equilibrium Propagation yields FID scores comparable to backpropagation, marking the first competitive CIFAR‑10 generative model trained without backpropagation.