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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…

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…

The time evolution of physical systems is described by differential equations, which depend on abstract quantities like energy and force. Traditionally, these quantities are derived as functionals based on observables such as positions and…

Simulating particle dynamics with high fidelity is crucial for solving real-world interaction and control tasks involving liquids in design, graphics, and robotics. Recently, data-driven approaches, particularly those based on graph neural…

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…

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…

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…

In many real world applications, data are characterized by a complex structure, that can be naturally encoded as a graph. In the last years, the popularity of deep learning techniques has renewed the interest in neural models able to…

Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our…

Neural networks (NNs) that exploit strong inductive biases based on physical laws and symmetries have shown remarkable success in learning the dynamics of physical systems directly from their trajectory. However, these works focus only on…

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.…

Deep learning models are able to approximate one specific dynamical system but struggle at learning generalisable dynamics, where dynamical systems obey the same laws of physics but contain different numbers of elements (e.g., double- and…

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…

Lagrangian Neural Networks (LNNs) present a principled and interpretable framework for learning the system dynamics by utilizing inductive biases. While traditional dynamics models struggle with compounding errors over long horizons, LNNs…

When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…

Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the…

In this paper, we present a comprehensive evaluation to establish a robust and efficient framework for Lagrangian-based particle tracing using deep neural networks (DNNs). Han et al. (2021) first proposed a DNN-based approach to learn…

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…

By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…

Neural networks with physics based inductive biases such as Lagrangian neural networks (LNN), and Hamiltonian neural networks (HNN) learn the dynamics of physical systems by encoding strong inductive biases. Alternatively, Neural ODEs with…