arXiv research

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

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

Conserved quantities on multisymplectic manifolds extend symplectic geometry results.

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.

Study finds conservation laws for maps on spheres.

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.

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.

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.

The paper explores symmetries and conservation laws in Hamiltonian systems.

RORL improves offline RL robustness with conservative smoothing.

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

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…

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

Discover conservation laws from trajectories using a neural network.

The paper extends geometric study to systems of PDEs, introducing variational bi-complex for conservation laws.

Study connects surface classes to conservation laws.

Adaptive design reduces uncertainty for conservative excursion set estimation.

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

The study characterizes polynomial conserved quantities for Lie applicable surfaces.

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.

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

A new algorithm for contextual combinatorial bandits reduces regret.

Defines special classes of constrained Willmore surfaces using polynomial conserved quantities.

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…