Related papers: Combining Physics and Deep Learning to learn Conti…

A physics-informed neural network is presented for poroelastic problems with coupled flow and deformation processes. The governing equilibrium and mass balance equations are discussed and specific derivations for two-dimensional cases are…

Model-based reinforcement learning (MBRL) is believed to have much higher sample efficiency compared to model-free algorithms by learning a predictive model of the environment. However, the performance of MBRL highly relies on the quality…

We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for…

In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural…

In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from…

Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear…

Despite the phenomenal success of deep learning in recent years, there remains a gap in understanding the fundamental mechanics of neural nets. More research is focussed on handcrafting complex and larger networks, and the design decisions…

Video representation learning has recently attracted attention in computer vision due to its applications for activity and scene forecasting or vision-based planning and control. Video prediction models often learn a latent representation…

Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian…

We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…

The deep linear network (DLN) is a model for implicit regularization in gradient based optimization of overparametrized learning architectures. Training the DLN corresponds to a Riemannian gradient flow, where the Riemannian metric is…

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…

Modelling robot dynamics accurately is essential for control, motion optimisation and safe human-robot collaboration. Given the complexity of modern robotic systems, dynamics modelling remains non-trivial, mostly in the presence of…

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

Deep neural networks can struggle to learn continually in the face of non-stationarity. This phenomenon is known as loss of plasticity. In this paper, we identify underlying principles that lead to plastic algorithms. In particular, we…

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Bridging the gap between motion models and reality is crucial by using limited data to deploy robots in the real world. Deep learning is expected to be generalized to diverse situations while reducing feature design costs through end-to-end…

In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…

Deep neural networks are widely used for classification. These deep models often suffer from a lack of interpretability -- they are particularly difficult to understand because of their non-linear nature. As a result, neural networks are…