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Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
The electrochemical reduction of atmospheric CO$_2$ into high-energy molecules with renewable energy is a promising avenue for energy storage that can take advantage of existing infrastructure especially in areas where sustainable…
Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…
This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…
Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be…
Smoothed dissipative particle dynamics (SDPD) is a widely used particle-based method for modelling soft matter systems at mesoscopic and macroscopic scales, offering thermodynamic consistency and direct control over the fluid's transport…
This paper presents a novel stochastic method for modeling the transport of Delayed Neutron Precursors (DNPs) in liquid nuclear fuel. The method incorporates advection and diffusion effects into the Monte Carlo solution of the neutron…
Generative models have the potential to accelerate key steps in the discovery of novel molecular therapeutics and materials. Diffusion models have recently emerged as a powerful approach, excelling at unconditional sample generation and,…
Denoising diffusion models trained at web-scale have revolutionized image generation. The application of these tools to engineering design is an intriguing possibility, but is currently limited by their inability to parse and enforce…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
Exploiting pre-trained diffusion models for restoration has recently become a favored alternative to the traditional task-specific training approach. Previous works have achieved noteworthy success by limiting the solution space using…
Integration of physics principles with data-driven methods has attracted great attention in recent few years. In this study, a physics-informed dynamic mode decomposition (piDMD) method, where the mass conservation law is integrated with a…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
Motivated by a problem in heterogeneous catalysis, we study a model for irreversible first-order reactions in which gas transport occurs only by diffusion, and reaction occurs only at a small number of well-localized sites. The main problem…
A significant drawback of Lagrangian (particle-tracking) reactive transport models has been their inability to properly simulate interactions between solid and liquid chemical phases, such as dissolution and precipitation reactions. This…
Diffusion models have demonstrated strong generative capabilities across scientific domains, but often produce outputs that violate physical laws. We propose a new perspective by framing physics-informed generation as a sparse reward…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…
With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs). Compared to traditional methods, PINNs…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
The ability to predict the future trajectories of traffic participants is crucial for the safe and efficient operation of autonomous vehicles. In this paper, a diffusion-based generative model for multi-agent trajectory prediction is…