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Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…
Elucidating reaction mechanisms hinges on efficiently generating transition states (TSs), products, and complete reaction networks. Recent generative models, such as diffusion models for TS sampling and sequence-based architectures for…
Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory…
The advent of single-cell technology has significantly improved our understanding of cellular states and subpopulations in various tissues under normal and diseased conditions by employing data-driven approaches such as clustering and…
Diffusion and flow matching models generate samples by learning time-dependent vector fields whose integration transports noise to data, requiring tens to hundreds of network evaluations at inference. We instead learn the transport map…
In this work, we investigate a method for simulation-free training of Neural Ordinary Differential Equations (NODEs) for learning deterministic mappings between paired data. Despite the analogy of NODEs as continuous-depth residual…
We propose a new abstraction set (SynopSet) that has a continuum of visual representations for the explanatory analysis of molecular dynamics simulations (MDS) in the DNA nanotechnology domain. By re-purposing the commonly used progress bar…
We develop a Spatio-TEMporal Mutually Exciting point process with Dynamic network (STEMMED), i.e., a point process network wherein each node models a unique community-drug event stream with a dynamic mutually-exciting structure, accounting…
Accurate forecasting of energy demand and supply is critical for optimizing sustainable energy systems, yet it is challenged by the variability of renewable sources and dynamic consumption patterns. This paper introduces a neural framework…
Real-world time series analysis faces significant challenges when dealing with irregular and incomplete data. While Neural Differential Equation (NDE) based methods have shown promise, they struggle with limited expressiveness, scalability…
Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
Social networks represent a common form of interconnected data frequently depicted as graphs within the domain of deep learning-based inference. These communities inherently form dynamic systems, achieving stability through continuous…
We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…
Neural Ordinary Differential Equations (NeuralODEs) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences.…
Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…
Biological processes, functions, and properties are intricately linked to the ensemble of protein conformations, rather than being solely determined by a single stable conformation. In this study, we have developed P2DFlow, a generative…
Despite their elegant formulation and lightweight memory cost, neural ordinary differential equations (NODEs) suffer from known representational limitations. In particular, the single flow learned by NODEs cannot express all homeomorphisms…
Understanding and modeling nonlinear dynamical systems is a fundamental challenge across science and engineering. Deep learning has shown remarkable potential for capturing complex system behavior, yet achieving models that are both…
The present project aims to use machine learning, specifically neural networks (NN), to learn the trajectories of a set of coupled ordinary differential equations (ODEs) and decrease compute times for obtaining ODE solutions by using this…