Related papers: Continuous Forecasting via Neural Eigen Decomposit…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
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…
Multi-agent trajectory prediction is crucial for various practical applications, spurring the construction of many large-scale trajectory datasets, including vehicles and pedestrians. However, discrepancies exist among datasets due to…
Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…
Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE),…
Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…
Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with…
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…
Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…
Stochastic differential equations (SDEs) have been widely used to model real world random phenomena. Existing works mainly focus on the case where the time series is modeled by a single SDE, which might be restrictive for modeling time…
Long-horizon motion forecasting for multiple autonomous robots is challenging due to non-linear agent interactions, compounding prediction errors, and continuous-time evolution of dynamics. Learned dynamics of such a system can be useful in…
Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…
The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…
Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generations of neural networks with capability of learning maps…
Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…