Related papers: Keep the Momentum: Conservation Laws beyond Euclid…
The paper surveys recent progresses in understanding the dynamics and loss landscape of the gradient flow equations associated to deep linear neural networks, i.e., the gradient descent training dynamics (in the limit when the step size…
Motivated by the growing use of artificial intelligence (AI) tools in control design, this paper analyses the intersection between results from gradient methods for the model-free linear quadratic regulator (LQR), and linear feedforward…
The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the…
Fast and accurate structural dynamics analysis is important for structural design and damage assessment. Structural dynamics analysis leveraging machine learning techniques has become a popular research focus in recent years. Although the…
Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external…
In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…
We prove that smooth solutions of non-ideal (viscous and resistive) incompressible magnetohydrodynamic equations satisfy a stochastic law of flux conservation. This property involves an ensemble of surfaces obtained from a given, fixed…
A case can be made that the utility of quasi-linear systems of conservation laws as physical models is largely limited to Euler system models of fluid flow, at least in higher dimensions. Qualified corroboration of this conjecture is…
Understanding implicit bias of gradient descent for generalization capability of ReLU networks has been an important research topic in machine learning research. Unfortunately, even for a single ReLU neuron trained with the square loss, it…
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…
Implicit deep learning has received increasing attention recently due to the fact that it generalizes the recursive prediction rules of many commonly used neural network architectures. Its prediction rule is provided implicitly based on the…
Learning a task induces connectivity changes in neural circuits, thereby changing their dynamics. To elucidate task related neural dynamics we study trained Recurrent Neural Networks. We develop a Mean Field Theory for Reservoir Computing…
The paper aims to study the connection between symmetries and conservation laws for the 2D Ricci flow model. The procedure starts by obtaining a set of multipliers which generates conservation laws. Then, using a general relation which…
The "ratchet principle", which states that non-equilibrium systems violating parity symmetry generically exhibit steady-state currents, is one of the few generic results outside thermal equilibrium. We study exceptions to this principle…
Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open…
Contraction metrics are crucial in control theory because they provide a powerful framework for analyzing stability, robustness, and convergence of various dynamical systems. However, identifying these metrics for complex nonlinear systems…
We consider chiral fluids within the standard framework of a chiral-invariant underlying field theory, anomalous in presence of electromagnetic fields. Apart from the Noether axial current of the underlying theory, in the limit of ideal…
We derive conservation laws for energy-momentum (canonical and dynamical) and angular momentum for a general Lorentz connection.
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with…
The conservation laws of electromagnetism, and implicitly all theories built from quadratic Lagrangians, are extended to a continuum of nonlocal versions. These are associated with symmetries of a class of equal time field correlation…