Related papers: Discovering interpretable Lagrangian of dynamical …

Lagrangian Neural Networks (LNNs) can learn arbitrary Lagrangians from trajectory data, but their unusual optimization objective leads to significant training instabilities that limit their application to complex systems. We propose several…

Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum. We…

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…

Reconstructions of Lagrangian drift, for example for objects lost at sea, are often uncertain due to unresolved physical phenomena within the data. Uncertainty is usually overcome by introducing stochasticity into the drift, but this…

Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…

Learning disentangled representations is a key step towards effectively discovering and modelling the underlying structure of environments. In the natural sciences, physics has found great success by describing the universe in terms of…

We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…

Distilling interpretable physical laws from videos has led to expanded interest in the computer vision community recently thanks to the advances in deep learning, but still remains a great challenge. This paper introduces an end-to-end…

Physical dynamical systems can be viewed as natural information processors: their systems preserve, transform, and disperse input information. This perspective motivates learning not only from data generated by such systems, but also how to…

Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…

We study aleatoric and epistemic uncertainty estimation in a learned regressive system dynamics model. Disentangling aleatoric uncertainty (the inherent randomness of the system) from epistemic uncertainty (the lack of data) is crucial for…

We develop a systematic information-theoretic framework for quantification and mitigation of error in probabilistic Lagrangian (i.e., path-based) predictions which are obtained from dynamical systems generated by uncertain (Eulerian) vector…

The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…

We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…

Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space…

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Recently, many reinforcement learning techniques were shown to have provable guarantees in the simple case of linear dynamics, especially in problems like linear quadratic regulators. However, in practice, many reinforcement learning…

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…