Related papers: Modular Neural Ordinary Differential Equations
To understand the fundamental trade-offs between training stability, temporal dynamics and architectural complexity of recurrent neural networks~(RNNs), we directly analyze RNN architectures using numerical methods of ordinary differential…
Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the…
This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one…
Neural differential equations offer a powerful framework for modeling continuous-time dynamics, but forecasting stiff biophysical systems remains unreliable. Standard Neural ODEs and physics informed variants often require orders of…
Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…
Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…
Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While…
Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…
Neural networks can be used to learn the solution of partial differential equations (PDEs) on arbitrary domains without requiring a computational mesh. Common approaches integrate differential operators in training neural networks using a…
Natural laws are often described through differential equations yet finding a differential equation that describes the governing law underlying observed data is a challenging and still mostly manual task. In this paper we make a step…
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…
Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…
Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…
With the shift towards decentralized energy generation, the increasing complexity of power systems renders physics-based modeling challenging. At the same time the growing amount of available measurement data opens the door for obtaining…
Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each…
Neural operators are a popular technique in scientific machine learning to learn a mathematical model of the behavior of unknown physical systems from data. Neural operators are especially useful to learn solution operators associated with…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
Pneumatic artificial muscles (PAMs) enable compliant actuation for soft wearable, assistive, and interactive robots. When arranged antagonistically, PAMs can provide variable impedance through co-contraction but exhibit coupled, nonlinear,…
Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging,…