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Recently, deep residual networks have been successfully applied in many computer vision and natural language processing tasks, pushing the state-of-the-art performance with deeper and wider architectures. In this work, we interpret deep…

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…

Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often…

Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their…

Poverty is a complex dynamic challenge that cannot be adequately captured using predefined differential equations. Nowadays, artificial machine learning (ML) methods have demonstrated significant potential in modelling real-world dynamical…

We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates Time-Integrated Deep Operator Networks (TI-DeepONets) as differentiable PDE surrogate models within the Differentiable Predictive…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…

Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator…

Embedding is a useful technique to project a high-dimensional feature into a low-dimensional space, and it has many successful applications including link prediction, node classification and natural language processing. Current approaches…

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…

Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

Spiking Neural Networks (SNNs) draw inspiration from biological neurons to enable brain-like computation, demonstrating effectiveness in processing temporal information with energy efficiency and biological realism. Most existing SNNs are…

Memristors have emerged as ideal components for modeling synaptic connections in neural networks due to their ability to emulate synaptic plasticity and memory effects. Discrete models of memristor-coupled neurons are crucial for…

We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…

Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…

The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles. However, deciphering the numerical integration in Neural ODE is…

Designing effective neural networks requires tuning architectural elements. This study integrates fractional calculus into neural networks by introducing fractional order derivatives (FDO) as tunable parameters in activation functions,…

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…