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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…

Understanding natural symmetries is key to making sense of our complex and ever-changing world. Recent work has shown that neural networks can learn such symmetries directly from data using Hamiltonian Neural Networks (HNNs). But HNNs…

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks.…

Incorporating neural networks for the solution of Ordinary Differential Equations (ODEs) represents a pivotal research direction within computational mathematics. Within neural network architectures, the integration of the intrinsic…

Deep Neural Networks (DNNs) excel at many tasks, often rivaling or surpassing human performance. Yet their internal processes remain elusive, frequently described as "black boxes." While performance can be refined experimentally, achieving…

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…

The existence or not of pathologies in the context of Lagrangian theory is studied with the aid of Machine Learning algorithms. Using an example in the framework of classical mechanics, we make a proof of concept, that the construction of…

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…

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…

Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey…

Deep neural networks (DNN) are increasingly being used to learn controllers due to their excellent approximation capabilities. However, their black-box nature poses significant challenges to closed-loop stability guarantees and performance…

By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a…

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…

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem…

In addition to being extremely non-linear, modern problems require millions if not billions of parameters to solve or at least to get a good approximation of the solution, and neural networks are known to assimilate that complexity by…

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…

Deep neural networks (DNN) are black box algorithms. They are trained using a gradient descent back propagation technique which trains weights in each layer for the sole goal of minimizing training error. Hence, the resulting weights cannot…

The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…

We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…