7 papers
Sparse Random-Feature Neural Networks with Krylov-Based SVD for Singularly Perturbed ODE
Kevin Kurian Thomas Vaidyan, Siddharth Rout
Random-feature neural networks (RFNNs), including architectures with fixed hidden layers and analytically determined output weights, offer fast training but often suffer from issue…
PDE-SSM: A Spectral State Space Approach to Spatial Mixing in Diffusion Transformers
Eshed Gal, Moshe Eliasof, Siddharth Rout +1
The success of vision transformers-especially for generative modeling-is limited by the quadratic cost and weak spatial inductive bias of self-attention. We propose PDE-SSM, a spat…
Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting
Carlos A. Pereira, Stéphane Gaudreault, Valentin Dallerit +9
Machine-learning approaches to weather forecasting often employ a monolithic architecture in which distinct physical mechanisms, such as advection, diffusive mixing, thermodynamic…
Fast, Convex and Conditioned Network for Multi-Fidelity Vectors and Stiff Univariate Differential Equations
Siddharth Rout
Accuracy in neural PDE solvers often breaks down not because of limited expressivity, but due to poor optimisation caused by ill-conditioning, especially in multi-fidelity and stif…
Fast and Flexible Probabilistic Forecasting of Dynamical Systems using Flow Matching and Physical Perturbation
Siddharth Rout, Eldad Haber, Stephane Gaudreault
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble…
Probabilistic Forecasting for Dynamical Systems with Missing or Imperfect Data
Siddharth Rout, Eldad Haber, Stéphane Gaudreault
The modeling of dynamical systems is essential in many fields, but applying machine learning techniques is often challenging due to incomplete or noisy data. This study introduces…
Advection Augmented Convolutional Neural Networks
Niloufar Zakariaei, Siddharth Rout, Eldad Haber +1
Many problems in physical sciences are characterized by the prediction of space-time sequences. Such problems range from weather prediction to the analysis of disease propagation a…