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Data-driven modeling of physical systems often relies on learning both positions and momenta to accurately capture Hamiltonian dynamics. However, in many practical scenarios, only position measurements are readily available. In this work,…

Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…

Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by…

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…

Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Hybrid machine learning combines physical knowledge with data-driven models to enhance interpretability and performance. In this context, Port-Hamiltonian Systems (PHS), which generalize Hamiltonian mechanics to describe open,…

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…

Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

We propose a hybrid meta-learning framework for forecasting and anomaly detection in nonlinear dynamical systems characterized by nonstationary and stochastic behavior. The approach integrates a physics-inspired simulator that captures…

Neural ODE Processes approach the problem of meta-learning for dynamics using a latent variable model, which permits a flexible aggregation of contextual information. This flexibility is inherited from the Neural Process framework and…

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…