arXiv research

Proposes a conservative exploration method for RL agents.

This work connects symmetries and conserved quantities in machine learning.

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 …

A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e. posi…

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

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

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

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

Survey on conservation laws for geometric PDEs.

A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.

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

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

I consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such equations. This provides an auxiliary differential equation satisfied by the conservatio…

This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87 (1997), 265-319]. The constrained variational bi-complex is introduced and used to d…

Non-trivial conservation law found for a specific system.

Symmetry-regularized Neural ODEs improve model stability and interpretability.

Gaussian process model learns Hamiltonian systems from noisy data.

Conservation law for weakly harmonic mappings in high dimensions.

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 …

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…

BCPO optimizes offline RL policies by converting uncertainty into conservative bounds.

VaR-CPO optimizes VaR-constrained RL problems with conservative policy updates.

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…

Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which admit potential symmetries. Then by using the partial Lagrangian approach, we fi…

New conservation laws found for polyharmonic maps in critical dimension.

The paper tackles safe exploration in RL by a conservative safety critic.

LNNs learn Lagrangians without canonical coordinates, conserving energy and relativity.

Develops ECD framework for optimizing machine learning problems.

A challenging problem in complex networks is the network reconstruction problem from data. This work deals with a class of networks denoted as conserved networks, in which a flow associated with every edge and the flows are conserved at all non-source and non-sink nodes. We propose a novel polynomial time algorithm to …

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

Unified neural network framework for context-aware Gaussian overbounds in uncertainty propagation.

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

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…

Noether's Theorem yields conservation laws for a Lagrangian 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. The aim of this paper is to explain the mathematical structure of both the Euler…

CQL learns conservative Q-functions to improve offline RL performance.

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

We consider the problem of estimating the set of all inputs that leads a system to some particular behavior. The system is modeled by an expensive-to-evaluate function, such as a computer experiment, and we are interested in its excursion set, i.e. the set of points where the function takes values above or below some p…

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…

The network jackknife provides conservative variance estimates for network statistics.

In this paper we study the relation between conserved quantities of nonholonomic systems and the hamiltonization problem employing the geometric methods of [1,3]. We illustrate the theory with classical examples describing the dynamics of solids of revolution rolling without sliding on a plane. In these cases, using th…

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…

Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a reduced model of such complex systems on the basis of insights alone. We propose a nov…

Data symmetries in neural networks can generate conserved quantities.

RORL improves offline RL robustness with conservative smoothing.

Canary optimizes VaR-constrained RL problems with a conservative bound using Cantelli's inequality.

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…