Related papers: PHDME: Physics-Informed Diffusion Models without E…
For many systems in science and engineering, the governing differential equation is either not known or known in an approximate sense. Analyses and design of such systems are governed by data collected from the field and/or laboratory…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural…
We propose an unsupervised anomaly detection approach based on a physics-informed diffusion model for multivariate time series data. Over the past years, diffusion model has demonstrated its effectiveness in forecasting, imputation,…
In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts…
Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
We present a latent diffusion-based differentiable inversion method (LD-DIM) for PDE-constrained inverse problems involving high-dimensional spatially distributed coefficients. LD-DIM couples a pretrained latent diffusion prior with an…
The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the…
Modeling rarefied hypersonic flows remains a fundamental challenge due to the breakdown of classical continuum assumptions in the transition-continuum regime, where the Knudsen number ranges from approximately 0.1 to 10. Conventional…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
This Letter introduces an approach for precisely designing surface friction properties using a conditional generative machine learning model, specifically a diffusion denoising probabilistic model (DDPM). We created a dataset of synthetic…
Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…
Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…
The performance of optimization-based robot motion planning algorithms is highly dependent on the initial solutions, commonly obtained by running a sampling-based planner to obtain a collision-free path. However, these methods can be slow…
Diffusion Probabilistic Models (DPMs) have recently shown remarkable performance in image generation tasks, which are capable of generating highly realistic images. When adopting DPMs for image restoration tasks, the crucial aspect lies in…
Pore-scale simulations accurately describe transport properties of fluids in the subsurface. These simulations enhance our understanding of applications such as assessing hydrogen storage efficiency and forecasting CO$_2$ sequestration…
Training deep learning methods on small time series datasets that also include corrupted samples is challenging. Diffusion models have shown to be effective to generate realistic and synthetic data, and correct corrupted samples through…
We propose masked particle modeling (MPM) as a self-supervised method for learning generic, transferable, and reusable representations on unordered sets of inputs for use in high energy physics (HEP) scientific data. This work provides a…