Related papers: Data-driven Prediction of General Hamiltonian Dyna…

We reveal the symplectic nature of parameter-drift maps by embedding them into extended phase space. Applying the embedding to the parameter-drift standard nontwist map, our construction yields an autonomous symplectic map in extended phase…

Data-driven learning of physical systems has kindled significant attention, where many neural models have been developed. In particular, mesh-based graph neural networks (GNNs) have demonstrated significant potential in modeling…

World models have recently re-emerged as a central paradigm for embodied intelligence, robotics, autonomous driving, and model-based reinforcement learning. However, current world model research is often dominated by three partially…

Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…

Graph neural networks (GNNs) have achieved success in various inference tasks on graph-structured data. However, common challenges faced by many GNNs in the literature include the problem of graph node embedding under various geometries and…

There is a recent surge in the development of spatio-temporal forecasting models in the transportation domain. Long-range traffic forecasting, however, remains a challenging task due to the intricate and extensive spatio-temporal…

The past decade has amply demonstrated the remarkable functionality that can be realized by learning complex input/output relationships. Algorithmically, one of the most important and opaque relationships is that between a problem's…

Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited.…

The rapid development of deep learning has significant implications for the advancement of Computational Fluid Dynamics (CFD). Currently, most pixel-grid-based deep learning methods for flow field prediction exhibit significantly reduced…

Causal discovery from observational data is challenging, especially with large datasets and complex relationships. Traditional methods often struggle with scalability and capturing global structural information. To overcome these…

Simulation-Grounded Neural Networks (SGNNs) are predictive models trained entirely on synthetic data from mechanistic simulations. They have achieved state-of-the-art performance in domains where real-world labels are limited or unobserved,…

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…

We introduce an approach for imposing physically informed inductive biases in learned simulation models. We combine graph networks with a differentiable ordinary differential equation integrator as a mechanism for predicting future states,…

Accelerated gradient methods have had significant impact in machine learning -- in particular the theoretical side of machine learning -- due to their ability to achieve oracle lower bounds. But their heuristic construction has hindered…

Precision soil greenhouse gas (GHG) flux prediction is essential in agricultural systems for assessing environmental impacts, developing emission mitigation strategies and promoting sustainable agriculture. Due to the lack of advanced…

We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…

Autonomous driving requires an understanding of the static environment from sensor data. Learned Bird's-Eye View (BEV) encoders are commonly used to fuse multiple inputs, and a vector decoder predicts a vectorized map representation from…

In this paper, we develop a neural network-based approach for time-series prediction in unknown Hamiltonian dynamical systems. Our approach leverages a surrogate model and learns the system dynamics using generalized coordinates (positions)…

We propose Symplectic Recurrent Neural Networks (SRNNs) as learning algorithms that capture the dynamics of physical systems from observed trajectories. An SRNN models the Hamiltonian function of the system by a neural network and…