Related papers: Deepmechanics

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks…

Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of…

This paper presents a framework for physics-informed learning in complex cyber-physical systems governed by differential equations with both unknown dynamics and algebraic invariants. First, we formalize the Hybrid Recurrent…

Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are…

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…

The last few years have witnessed an increased interest in incorporating physics-informed inductive bias in deep learning frameworks. In particular, a growing volume of literature has been exploring ways to enforce energy conservation while…

The effectiveness of the Physics Informed Neural Networks (PINNs) for learning the dynamics of constrained Hamiltonian systems is demonstrated using the Dirac theory of constraints for regular systems with holonomic constraints and systems…

Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in…

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based…

We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…

Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…

Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…

Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world…

Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…

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…

We introduce \emph{Dynamical Physics-Modeled Neural Networks} (DynPMNNs), a continuous-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation. Unlike classical feed-forward…

Lagrangian and Hamiltonian neural networks (LNNs and HNNs, respectively) encode strong inductive biases that allow them to outperform other models of physical systems significantly. However, these models have, thus far, mostly been limited…

This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple…

We present a five-module pedagogical framework for teaching physics-informed machine learning (ML) through two progressively complex physical systems: a driven, damped nonlinear pendulum and a one-dimensional quantum anharmonic oscillator.…