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Training-Loss Guarantees for Muon with Finite-Step Newton--Schulz Orthogonalization
Amartya Roy, Souvik Chakraborty
Existing convergence analyses of Muon either assume exact orthogonalization or analyze classical Newton--Schulz polynomials, and guarantee only stationarity, so it is unresolved wh…
Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs
Rajat Sarkar, Venkataramana Runkana, Souvik Chakraborty
Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical states. Learning these maps is d…
See, Hypothesize, Validate: Multimodal Agentic Framework for Discovering Governing PDEs
Sarang Manoj Pekhale, Amartya Roy, Rajat Sarkar +1
Discovering governing partial differential equations (PDEs) from observational data remains a core challenge across the sciences. Existing sparse-regression, symbolic-regression, a…
Towards Data-Efficient Cross-Device Generalization of Grad-Shafranov Equilibria via Transfer Learning Neural Operator
Jay Phil Yoo, William Howes, Yashika Ghai +3
Real-time reconstruction of magnetohydrodynamic equilibria is essential for plasma shaping, stability assessment and feedback control in magnetic confinement fusion. However, Grad-…
Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator
William Howes, Jason Yoo, Kazuma Kobayashi +4
Real-time inference of inaccessible interior physical fields from sparse boundary observations is a fundamental but unresolved problem in scientific machine learning, with direct r…
Stochastic Smoothed Particle Hydrodynamics for Stochastic Mechanics Problems
Mridul Tiwari, Sawan Kumar, Md Rushdie Ibne Islam +1
Smoothed Particle Hydrodynamics (SPH_ is a mesh-free Lagrangian method renowned for modeling large deformations and free-surface flows, yet classical formulations remain confined t…
Beyond Uniform Sampling: Synergistic Active Learning and Input Denoising for Robust Neural Operators
Samrendra Roy, Souvik Chakraborty, Syed Bahauddin Alam
Neural operators have emerged as fast surrogate models for physics simulations, yet they remain acutely vulnerable to adversarial perturbations, a critical liability for safety-cri…
SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving
Samrendra Roy, Souvik Chakraborty, Rizwan-uddin +1
Neural operators have emerged as powerful surrogates for partial differential equation (PDE) solvers, yet they are typically trained as monolithic models for individual PDEs, requi…
Learning the Stellar Structure Equations via Self-supervised Physics-Informed Neural Networks
Manuel Ballester, Santiago Lopez-Tapia, Seth Gossage +9
Stellar astrophysics relies critically on accurate descriptions of the physical conditions inside stars. Traditional solvers such as \texttt{MESA} (Modules for Experiments in Stell…
Scalable Random Wavelet Features: Efficient Non-Stationary Kernel Approximation with Convergence Guarantees
Sawan Kumar, Souvik Chakraborty
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simpl…