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Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions,…
The Fluid Antenna System (FAS) overcomes the spatial degree-of-freedom limitations of conventional static antenna arrays in wireless communications.This capability critically depends on acquiring full Channel State Information across all…
Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…
Coarse-grained (CG) molecular simulations have become a standard tool to study molecular processes on time- and length-scales inaccessible to all-atom simulations. Parameterizing CG force fields to match all-atom simulations has mainly…
Flow Matching (FM) is an effective framework for training a model to learn a vector field that transports samples from a source distribution to a target distribution. To train the model, early FM methods use random couplings, which often…
Recent endeavors aimed at forecasting future traffic flow states through deep learning encounter various challenges and yield diverse outcomes. A notable obstacle arises from the substantial data requirements of deep learning models, a…
The free energetics of water density fluctuations near a surface, and the rare low-density fluctuations in particular, serve as reliable indicators of surface hydrophobicity; the easier it is to displace the interfacial waters, the more…
Free energy landscapes provide insights into conformational ensembles of biomolecules. In order to analyze these landscapes and elucidate mechanisms underlying conformational changes, there is a need to extract metastable states with…
Flow and diffusion models achieve high-fidelity, high-resolution image synthesis, but often require many function evaluations (NFEs) at sampling time. Existing acceleration methods either require additional training through distillation or…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…
Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions $p_t$. We identify a geometric optimization bottleneck in this regression problem: when the covariance $\Sigma_t$ of $p_t$ is…
Conditional Flow Matching (CFM), a simulation-free method for training continuous normalizing flows, provides an efficient alternative to diffusion models for key tasks like image and video generation. The performance of CFM in solving…
While flow matching is elegant, its reliance on single-sample conditional velocities leads to high-variance training targets that destabilize optimization and slow convergence. By explicitly characterizing this variance, we identify 1) a…
We study channel simulation and distributed matching, two fundamental problems with several applications to machine learning, using a recently introduced generalization of the standard rejection sampling (RS) algorithm known as Ensemble…
Computational fluid dynamics (CFD) analysis is widely used in engineering. Although CFD calculations are accurate, the computational cost associated with complex systems makes it difficult to obtain empirical equations between system…
Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…
We describe a method to explore the configurational phase space of chemical systems. It is based on the nested sampling algorithm recently proposed by Skilling [Skilling J. (2004) In AIP Conference Proceedings, vol. 735, p. 395.; Skilling…
3D Gaussian Splatting (3DGS) has achieved excellent rendering quality with fast training and rendering speed. However, its optimization process lacks explicit geometric constraints, leading to suboptimal geometric reconstruction in regions…
Machine learning model development in chemistry and materials science often grapples with the challenge of small scale, unbalanced labelled datasets, a common limitation in scientific experiments. These dataset imbalances can precipitate…
Effective data partitioning is known to be crucial in machine learning. Traditional cross-validation methods like K-Fold Cross-Validation (KFCV) enhance model robustness but often compromise generalisation assessment due to high…