Model Reduction and Neural Networks

Reduced-observable dynamic mode decomposition for identifying theta and beta activity in working-memory EEG

This paper introduces a reduced-observable dynamic mode decomposition method for analyzing theta and beta EEG activity in working memory tasks, finding correlations between oscillatory power and memory encoding events.

Recovering Hidden Neural Oscillatory Modes from Partial Observations through Delay Embedding and Perturbation

This paper improves recovery of neural oscillatory modes from partial recordings using delay embedding and perturbation, showing increased mode estimates with deeper delay and perturbation.

A Physics-Informed Neural Network Surrogate for Patient-Specific Hepatic Arterial Hemodynamics in Yttrium-90 Radioembolization: Network Architecture, Boundary-Condition Enforcement, and Data Efficiency

This paper develops a physics-informed neural network surrogate for predicting hepatic arterial flow in Y-90 radioembolization, showing that data fraction is more critical than architecture for accuracy.

Inference of self-limiting neutrophil swarming dynamics using Bayesian physics-informed neural networks

The paper develops a Bayesian physics-informed neural network to model neutrophil swarming dynamics in human and murine cells, revealing species-specific differences in recruitment and self-limitation.

A metric for comparing complex systems by their dynamics

This paper introduces DSA, a metric to compare systems by their dynamics, showing it captures dynamical structure missed by geometric and topological methods.

CARDIAX-NNFE - A Cardiac Mechanics SciML Framework

The paper introduces CARDIAX-NNFE, a cardiac mechanics SciML framework that uses neural networks to simulate cardiac function with high accuracy and speed.

Dynamic Compression Flows for Neuroscience Data

This paper introduces a dual flow approach for modeling neural data, producing more interpretable dynamics and better reconstructions than existing methods.

Multi-stage physics-informed neural networks for JAK--STAT5 signaling and ultradian insulin--glucose dynamics: latent-species identifiability and suppression of parameter-induced divergence

This paper introduces a multi-stage physics-informed neural network to solve multi-species biochemical dynamics, demonstrating latent-species identifiability and suppression of parameter-induced divergence using synthetic data.

Physics-Informed Operator Learning for Pulsatile Milk Flow in Distal Generations of a Bifurcated Mammary Duct Network

This paper uses a physics-informed operator learning framework to predict pulsatile milk flow across a bifurcated mammary duct network, revealing key hemodynamic patterns in distal ducts.

Appellian Neural Networks

The paper introduces ANNet, a physics-informed neural network that unifies inverse and forward dynamics computations using a shared learned representation based on Appell's acceleration energy.

Learning dynamical systems with biochemically informed neural ordinary differential equations

The paper introduces BINODEs, a neural-ODE framework that integrates biochemical knowledge into dynamical models to improve interpretability and flexibility in modeling biochemical systems.

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.

Neural Network Guided Calibration for Fast Virtual Twin Generation in Cardiovascular ODE Models

This paper uses a neural network to rapidly calibrate a cardiovascular ODE model for virtual twin generation, showing it can achieve accurate results while being computationally efficient.

Modeling the inverse MEG problem in neuro-imaging using Physics Informed Neural Networks

This paper introduces a Physics-Informed Neural Network (PINN) framework for solving MEG forward and inverse problems, achieving a 30.2% improvement over standard Minimum Norm Estimation.

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.

Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation

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.

Data-Driven Reduced Modeling of Recurrent Neural Networks

This study uses data-driven methods to reduce the dimensionality of RNNs and identify core dynamics, leading to new insights into neuronal decision-making and memory.

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.

Time-series modeling with neural flow maps

This work introduces a deep learning framework to reconstruct flow maps from time-series data, demonstrating its effectiveness in capturing circadian transcriptomic dynamics across multiple organs.

Data-driven identification of biomedical systems using multi-scale analysis

The paper introduces a data-driven framework combining SINDy, CSP, and neural networks to identify reduced models of biomedical systems from observational data, demonstrating success on the Michaelis-Menten model.

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.

Conditional Universal Differential Equations Simultaneously Capture Population Level Dynamics and Inter-individual Variation in Human C-peptide Production

This paper introduces a conditional universal differential equation (cUDE) to model inter-individual variation in human c-peptide production across different glucose tolerance states.

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.

Deep graph convolutional neural network for one-dimensional hepatic vascular haemodynamic prediction

This paper proposes a deep graph neural network to predict one-dimensional hepatic vascular hemodynamics, achieving high accuracy and speed compared to CFD methods.

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.

Physiology-informed regularization enables training of universal differential equation systems for biological applications

This paper introduces physiology-informed regularization for universal differential equation models to improve accuracy and reduce data requirements in biological applications.

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.