Related papers: Learning Flame Evolution Operator under Hybrid Dar…
Fourier neural operators (FNOs) provide a mesh-independent way to learn solution operators for partial differential equations, yet their efficacy for magnetized turbulence is largely unexplored. Here we train an FNO surrogate for the 2-D…
In the present work, the discrete flame model [1] is augmented by introducing the thermal inertia of particles in the preheating zone. The effect of particle thermal inertia on flame speed, propagation limits, and near-limits dynamics of…
In recent years, Machine-Learning (ML)-driven approaches have been widely used in scientific discovery domains. Among them, the Fourier Neural Operator (FNO) was the first to simulate turbulent flow with zero-shot super-resolution and…
Laplace Neural Operators (LNOs) have recently emerged as a promising approach in scientific machine learning due to the ability to learn nonlinear maps between functional spaces. However, this framework often requires substantial amounts of…
Deep learning methods are emerging as popular computational tools for solving forward and inverse problems in traffic flow. In this paper, we study a neural operator framework for learning solutions to nonlinear hyperbolic partial…
Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…
Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…
We present a study of numerical behavior of a thickened flame used in Flame Capturing (FC, Khokhlov (1995)) for tracking thin unresolved physical flames in deflagration simulations. We develop a steady-state procedure for calibrating the…
This work presents a novel framework for physically consistent model error characterization and operator learning for reduced-order models of non-equilibrium chemical kinetics. By leveraging the Bayesian framework, we identify and infer…
The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning…
This study focuses on addressing the challenges of solving analytically intractable differential equations that arise in scientific and engineering fields such as Hamilton-Jacobi-Bellman. Traditional numerical methods and neural network…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
Long-term prediction of three-dimensional (3D) turbulent flows is one of the most challenging problems for machine learning approaches. Although some existing machine learning approaches such as implicit U-net enhanced Fourier neural…
Flame propagation through a non-volatile solid-fuel suspension is studied using a simplified, time-dependent numerical model that considers the influence of both diffusional and kinetic rates on the particle combustion process. It is…
Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire…
Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…
Interacting lattice Hamiltonians at high temperature generically give rise to energy transport governed by the classical diffusion equation; however, predicting the rate of diffusion requires numerical simulation of the microscopic quantum…
A nonlinear equation describing curved stationary flames with arbitrary gas expansion $\theta = \rho_{{\rm fuel}}/\rho_{{\rm burnt}}$, subject to the Landau-Darrieus instability, is obtained in a closed form without an assumption of weak…
We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…
We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…