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A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
In this paper, we investigate the influence of multiplicities in activity coefficients on batch distillation processes. In order to do so, we develop a rigorous simulation of batch distillation processes based on the MESH equations. In…
Diffusion models are the go-to method for Text-to-Image generation, but their iterative denoising processes has high inference latency. Quantization reduces compute time by using lower bitwidths, but applies a fixed precision across all…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
Autonomous driving requires reasoning about interactions with surrounding traffic. A prevailing approach is large-scale imitation learning on expert driving datasets, aimed at generalizing across diverse real-world scenarios. For online…
We report the development of a discontinuous spectral element flow solver that includes the implementation of both spectral difference and flux reconstruction formulations. With this high order framework, we have constructed a foundation…
The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and…
Unsupervised plain graph alignment (UPGA) aims to align corresponding nodes across two graphs without any auxiliary information. Existing UPGA methods rely on structural consistency while neglecting the inherent structural differences in…
We propose a methodology to infer collision operators from phase space data of plasma dynamics. Our approach combines a differentiable kinetic simulator, whose core component in this work is a differentiable Fokker-Planck solver, with a…
The design of inertial fusion experiments is a complex task as driver energy must be delivered in a precise manner to a structured target to achieve a fast, but hydrodynamically stable, implosion. Radiation-hydrodynamics simulation codes…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…
A computational procedure is developed for the efficient calculation of derivatives of integrals over non-separable Gaussian-type basis functions, used for the evaluation of gradients of the total energy in quantum-mechanical simulations.…
Our predictions for particle physics processes are realized in a chain of complex simulators. They allow us to generate high-fidelity simulated data, but they are not well-suited for inference on the theory parameters with observed data. We…
Reconstructing force fields (FFs) from atomistic simulation data is a challenge since accurate data can be highly expensive. Here, machine learning (ML) models can help to be data economic as they can be successfully constrained using the…
Diffusion models are a powerful generative framework, but come with expensive inference. Existing acceleration methods often compromise image quality or fail under complex conditioning when operating in an extremely low-step regime. In this…
Nonequilibrium, ``fast switching'' estimates of equilibrium free energy differences, Delta F, are often plagued by poor convergence due to dissipation. We propose a method to improve these estimates by generating trajectories with reduced…