Model Reduction and Neural Networks

A novel approach to quantify out-of-distribution uncertainty in Neural and Universal Differential Equations

This paper introduces a novel ensemble method for NODEs and UDEs to improve out-of-distribution uncertainty quantification in dynamical systems.

Transfer Learning Assessment of Data-driven Crystallisation Processes via Constrained Neural Ordinary Differential Equations

This paper assesses transfer learning for crystallisation modelling using constrained neural ODEs, showing improved generalisation and physical consistency in data-scarce scenarios.

BiLO: Bilevel Local Operator Learning for PDE Inverse Problems

The paper introduces BiLO, a neural network method for solving PDE inverse problems by formulating them as bilevel optimization problems, showing it enforces PDE constraints and handles noisy data effectively.

Dynamic mode decomposition for analysis and prediction of metabolic oscillations from time-lapse imaging of cellular autofluorescence

This paper applies dynamic mode decomposition to analyze and predict metabolic oscillations from time-lapse imaging of cellular autofluorescence, showing its effectiveness in capturing spatiotemporal dynamics.

Data-informed model reduction for inference and prediction from non-identifiable models

The paper presents a computational approach for reducing non-identifiable mathematical models using likelihood reparameterisation to enable efficient predictions.

Integrating Equation Coding with Residual Networks for Efficient ODE Approximation in Biological Research

This paper introduces LazyNet, a model using ResNet with logarithmic/exponential functions to approximate ODEs in biological systems, improving efficiency and reducing reliance on large datasets.

Data-driven model discovery and model selection for noisy biological systems

This paper introduces a framework for model discovery and selection in noisy biological systems using hybrid dynamical systems and neural networks, showing improved performance over existing methods.

Inferring in vivo murine cerebrospinal fluid flow using artificial intelligence velocimetry with moving boundaries and uncertainty quantification

This paper develops an AI velocimetry method to infer 3D CSF flow in mice, including pressure, shear stress, and flow rates, with uncertainty quantification.

Optimization-Based Synthesis with Directed Cell Migration

This work uses dynamic mode decomposition and optimal control theory to model collective cell migration and simulate single and multi-cellular systems, revealing mathematical rules and potential applications in therapeutic robotics.

Uncertainty quantified discovery of chemical reaction systems via Bayesian scientific machine learning

This paper introduces a Bayesian framework using neural ODEs and pSGLD to discover chemical reaction pathways with uncertainty quantification, showing improved accuracy over standard SGLD.

Non-Stationary Dynamic Mode Decomposition

This paper introduces Non-Stationary Dynamic Mode Decomposition (NS-DMD) to analyze time-varying spatiotemporal data, demonstrating its application to neural recordings from a non-human primate.

Data-Driven Flow-Map Models for Data-Efficient Discovery of Dynamics and Fast Uncertainty Quantification of Biological and Biochemical Systems

This paper introduces data-driven flow-map models for efficiently discovering dynamics and quantifying uncertainty in biochemical systems using polynomial chaos Kriging.