Related papers: Lagrangian Neural Networks for Reversible Dissipat…

Neural networks with physical governing equations as constraints have recently created a new trend in machine learning research. In line with such efforts, a deep learning model for one-dimensional consolidation where the governing equation…

We propose a method for training dynamical systems governed by Lagrangian mechanics using Equilibrium Propagation. Our approach extends Equilibrium Propagation - initially developed for energy-based models - to dynamical trajectories by…

The logarithmic divergence is an extension of the Bregman divergence motivated by optimal transport and a generalized convex duality, and satisfies many remarkable properties. Using the geometry induced by the logarithmic divergence, we…

Backpropagation is typically presented as a symbolic procedure: a backward pass topologically distinct from inference, with non-local error signals and synchronous global clocking, features with no clear analog in physical reality. Existing…

We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…

Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its…

Recent advancements in multi-modal large language models have propelled the development of joint probabilistic models capable of both image understanding and generation. However, we have identified that recent methods suffer from loss of…

Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…

Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…

Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network comprised of convolutional layers is a powerful tool for predicting…

A heavy top with a fixed point and a rigid body in an ideal fluid are important examples of Hamiltonian systems on a dual to the semidirect product Lie algebra $e(n)=so(n)\ltimes\mathbb R^n$. We give a Lagrangian derivation of the…

The equations of motion for a Lagrangian mainly refer to the acceleration equations, which can be obtained by the Euler--Lagrange equations. In the post-Newtonian Lagrangian form of general relativity, the Lagrangian systems can only…

Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…

This paper proposes a fractional order gradient method for the backward propagation of convolutional neural networks. To overcome the problem that fractional order gradient method cannot converge to real extreme point, a simplified…

We establish the Lagrangian nature of the discrete isospectral and isomonodromic dynamical systems corresponding to the re-factorization transformations of the rational matrix functions on the Riemann sphere. Specifically, in the…

We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…

Robotic systems operating in unstructured environments must operate under significant uncertainty arising from intermittent contacts, frictional variability, and unmodeled compliance. While recent model-free approaches have demonstrated…

We investigate how the theory of self-adjoint differential equations alone can be used to provide a satisfactory solution of the inverse vatiational problem. For the discrete system, the self-adjoint form of the Newtonian equation allows…

Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain…

In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle…