Related papers: Discovering conservation laws from trajectories vi…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the space over which a signal is defined. The model incorporates the…

Scientists have long aimed to discover meaningful formulae which accurately describe experimental data. A common approach is to manually create mathematical models of natural phenomena using domain knowledge, and then fit these models to…

Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data…

Constraint-based methods and noise-based methods are two distinct families of methods proposed for uncovering causal graphs from observational data. However, both operate under strong assumptions that may be challenging to validate or could…

Rotation invariance has been studied in the computer vision community primarily in the context of small in-plane rotations. This is usually achieved by building invariant image features. However, the problem of achieving invariance for…

Causal representation learning has emerged as the center of action in causal machine learning research. In particular, multi-domain datasets present a natural opportunity for showcasing the advantages of causal representation learning over…

Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long term prediction of the dynamics of the unknown system. In many real-world applications,…

Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of…

We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control.…

Assumptions about invariances or symmetries in data can significantly increase the predictive power of statistical models. Many commonly used models in machine learning are constraint to respect certain symmetries in the data, such as…

Continual learning is the problem of learning and retaining knowledge through time over multiple tasks and environments. Research has primarily focused on the incremental classification setting, where new tasks/classes are added at discrete…

We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data. We propose three modules and combine them to obtain two network architectures, coined R-VPNet and LA-VPNet. The…

Neurons can display highly variable dynamics. While such variability presumably supports the wide range of behaviors generated by the organism, their gene expressions are relatively stable in the adult brain. This suggests that neuronal…

Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra…

Dataset condensation aims to condense a large dataset with a lot of training samples into a small set. Previous methods usually condense the dataset into the pixels format. However, it suffers from slow optimization speed and large number…

While successful for various computer vision tasks, deep neural networks have shown to be vulnerable to texture style shifts and small perturbations to which humans are robust. In this work, we show that the robustness of neural networks…

We investigate the parameterization of deep neural networks that by design satisfy the continuity equation, a fundamental conservation law. This is enabled by the observation that any solution of the continuity equation can be represented…

We introduce a new strategy designed to help physicists discover hidden laws governing dynamical systems. We propose to use machine learning automatic differentiation libraries to develop hybrid numerical models that combine components…

Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network comprised of convolutional layers is a powerful tool for predicting…