arXiv research

Enhances water disaggregation for parallel appliances using shape features and Bayesian Discriminative Sparse Coding.

Machine learning improves ice flow tracking in satellite images.

Theoretical analysis confirms non-conservative algorithms can converge to optimal policies.

Study finds conservation laws for a specific class of parabolic equations.

Study finds conserved quantities for two types of curves on conformal sphere.

Survey on conservation laws for geometric PDEs.

The article discusses conservation laws for polyharmonic maps and their applications.

Algorithm reconstructs conserved networks from flow data.

Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.

Researchers found a geometric duality for systems of conservation laws.

Non-trivial conservation law found for a specific system.

This work connects symmetries and conserved quantities in machine learning.

Proposes a conservative exploration method for RL agents.

DEMUD-VIS detects novel image content and explains it visually.

The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation law has a unique representative. The structure of this subspace naturally gives …

Conservation law for weakly harmonic mappings in high dimensions.

Given a vector field on a manifold M, we define a globally conserved quantity to be a differential form whose Lie derivative is exact. Integrals of conserved quantities over suitable submanifolds are constant under time evolution, the Kelvin circulation theorem being a well-known special case. More generally, conserved…

We study higher-order conservation laws of the non-linearizable elliptic Poisson equation $\frac{{\partial}^2 u}{\partial z \partial \bar{z}} = -f(u)$ as elements of the characteristic cohomology of the associated exterior differential system. The theory of characteristic cohomology determines a normal form for diffe…

New conservation laws found for polyharmonic maps in critical dimension.

New variational principle found for PDEs with symmetries and conservation laws.

MC-LSTM extends LSTM to conserve mass in neural networks.

The paper studies symmetries and conservation laws of non-diagonalisable hydrodynamic systems.

Unified physics field theories through a general conservation law.

We present a connection between the Killing fields that arise in the loop-group approach to integrable systems and conservation laws viewed as elements of the characteristic cohomology. We use the connection to generate the complete set of conservation laws (as elements of the characteristic cohomology) for the Tzitzei…

A new algorithm balances exploration and exploitation in online decision-making.

We obtain necessary and sufficient conditions for the existence of "conservation laws" on null hypersurfaces for the wave equation on general four-dimensional Lorentzian manifolds. Examples of null hypersurfaces exhibiting such conservation laws include the standard null cones of Minkowski spacetime and the degenerate …

New neural network enforces mass conservation for better ice flow predictions.

The study finds resonance points in polarised curves with polynomial conserved quantities.

Following an approach of the second author for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and extrinsic biharmonic maps. With the help of this conservation law we prove the continuit…

There is a well-known example of integrable conservative system on $S^2$, the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. Goryachev proposed a one-parameter family of examples of conservative systems on $S^2$ possessing an integral of fourth degree in moment…

Data symmetries in neural networks can generate conserved quantities.

RORL improves offline RL robustness with conservative smoothing.

We propose a dynamical model for business cycle based on an optimal DI model. In the model there exists a conserved quantity, which corresponds to the total energy in a dynamical system. We found that the business cycle with the period 6 or 7 years is nicely reproduced, since the model predicts a periodic motion in the…

New definitions of conserved quantities at null infinity resolve ambiguities in general relativity.

This work extends balancing to various simulation-based inference algorithms for more conservative posterior approximations.

Discover conservation laws from trajectories using a neural network.

Study connects surface classes to conservation laws.

New framework models non-conservative stochastic processes without energy conservation constraints.

A new AI optimization method uses energy-conserving dynamics inspired by Born-Infeld theory.

Noether's First Theorem yields conservation laws for Lagrangians with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. In recent work the authors showed the mathematical structure behind both th…

Dan Reznik discovered conserved quantities for ellipses using billiard maps.

Framework infers conservation laws from trained neural networks.

A new algorithm for contextual combinatorial bandits reduces regret.

StepMix algorithm ensures safe exploration in reinforcement learning with near-optimal performance.

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant gauge--natural bundle this density is the divergence of a skew--symmetric (tenso…

Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closur…

In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will o…

New algorithms ensure policies perform at least as good as a baseline in reinforcement learning.