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This paper presents an efficient method based on Evolutionary Center Algorithm (ECA) for accurately and efficiently determining the optimal reaction and diffusion parameters for Chemical-Diffusive Models (CDM) to simulate flame acceleration…

Due to the unique channel characteristics of Terahertz (THz), comprehensive propagation channel modeling is essential to understand the spectrum and develop reliable communication systems in these bands. In this work, we propose the…

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…

Earth System Models (ESMs) are essential for understanding the interaction between human activities and the Earth's climate. However, the computational demands of ESMs often limit the number of simulations that can be run, hindering the…

Recent efforts on Diffusion Mixture-of-Experts (MoE) models have primarily focused on developing more sophisticated routing mechanisms. However, we observe that the underlying architectural configuration space remains markedly…

A supervised machine learning (ML) based computational methodology for the design of particulate multifunctional composite materials with desired thermal conductivity (TC) is presented. The design variables are physical descriptors of the…

Predicting microstructure evolution during thermomechanical treatment is essential for determining the final mechanical properties of a material, yet conventional simulations based on Partial Differential Equations (PDEs) remain…

We introduce Transfusion, a recipe for training a multi-modal model over discrete and continuous data. Transfusion combines the language modeling loss function (next token prediction) with diffusion to train a single transformer over…

Accurate molecular property prediction is central to drug discovery, catalysis, and process design, yet real-world applications are often limited by small datasets. Molecular foundation models provide a promising direction by learning…

Weather forecasting requires not only accuracy but also the ability to perform probabilistic prediction. However, deterministic weather forecasting methods do not support probabilistic predictions, and conversely, probabilistic models tend…

We present a general method for fitting finite mixture models (FMM). Learning in a mixture model consists of finding the most likely cluster assignment for each data-point, as well as finding the parameters of the clusters themselves. In…

Modern climate projections often suffer from inadequate spatial and temporal resolution due to computational limitations, resulting in inaccurate representations of sub-grid processes. A promising technique to address this is the Multiscale…

The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…

We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and…

Modeling of high-dimensional data is very important to categorize different classes. We develop a new mixture model called Multinomial cluster-weighted model (MCWM). We derive the identifiability of a general class of MCWM. We estimate the…

The usefulness of semi-analytical thermal models for predicting the connection between process, microstructure and properties in powder bed fusion has been well illustrated in recent years. Such an approach provides the promise of accuracy…

We develop clustering procedures for longitudinal trajectories based on a continuous-time hidden Markov model (CTHMM) and a generalized linear observation model. Specifically in this paper, we carry out finite and infinite mixture…

We develop a two-fluid model (TFM) for heat transfer in dense non-Brownian suspensions. Specifically, we propose closure relations for the inter-phase heat transfer coefficient and the thermal diffusivity of the particle phase based on…

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…

Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters…