Related papers: Studying Lagrangian theories with machine learning…
In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating…
Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy.…
Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the…
An activity fundamental to science is building mathematical models. These models are used to both predict the results of future experiments and gain insight into the structure of the system under study. We present an algorithm that…
Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily…
Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…
As a network-based functional approximator, we have proposed a "Lagrangian Density Space-Time Deep Neural Networks" (LDDNN) topology. It is qualified for unsupervised training and learning to predict the dynamics of underlying physical…
This article investigates the modeling and control of Lagrangian systems involving non-conservative forces using a hybrid method that does not require acceleration calculations. It focuses in particular on the derivation and identification…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
Physical systems are commonly represented as a combination of particles, the individual dynamics of which govern the system dynamics. However, traditional approaches require the knowledge of several abstract quantities such as the energy or…
Deep learning has achieved astonishing results on many tasks with large amounts of data and generalization within the proximity of training data. For many important real-world applications, these requirements are unfeasible and additional…
This study investigates the potential for biological systems to be governed by a variational principle, suggesting that such systems may evolve to minimize or optimize specific quantities. To explore this idea, we focus on identifying…
Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation…
Combining deep learning with classical physics facilitates the efficient creation of accurate dynamical models. In a recent class of neural network, Lagrangian mechanics is hard-coded into the architecture, and training the network learns…
The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
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…
Based on Darwin's natural selection, we developed "machine scientists" to discover the laws of nature by learning from raw data. "Machine scientists" construct physical theories by applying a logic tree (state Decision Tree) and a value…
Machine learning presents a general, systematic framework for the generation of formal theoretical models for physical description and prediction. Tentatively standard linear modeling techniques are reviewed; followed by a brief discussion…
We study the problem of building an efficient learning system. Efficient learning processes information in the least time, i.e., building a system that reaches a desired error threshold with the least number of observations. Building upon…