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Building a representative model of a complex system remains a highly challenging problem. While by now there is basic understanding of most physical domains, model design is often hindered by lack of detail, for example concerning model…
We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…
The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving processes, partially…
Although optimal control problems of dynamical systems can be formulated within the framework of variational calculus, their solution for complex systems is often analytically and computationally intractable. In this Letter we present a…
We introduce a new way of learning to encode position information for non-recurrent models, such as Transformer models. Unlike RNN and LSTM, which contain inductive bias by loading the input tokens sequentially, non-recurrent models are…
Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown…
Encoding a sequence of observations is an essential task with many applications. The encoding can become highly efficient when the observations are generated by a dynamical system. A dynamical system imposes regularities on the observations…
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 networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
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…
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…
Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should…
Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…
Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…
Data-driven methods are becoming an essential part of computational mechanics due to their unique advantages over traditional material modeling. Deep neural networks are able to learn complex material response without the constraints of…
There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…
This paper addresses imitation learning for motion prediction problem in autonomous driving, especially in multi-agent setting. Different from previous methods based on GAN, we present the conditional latent ordinary differential equation…
In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…
Predicting the behaviors of pedestrian crowds is of critical importance for a variety of real-world problems. Data driven modeling, which aims to learn the mathematical models from observed data, is a promising tool to construct models that…
Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…