arXiv research

Review and compare model order reduction methods for process engineering.

We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotangent, Lagrangian dynamics on tangent bundles and, both Hamiltonian and Lagrangian dynamics on Tulczyjew's symplectic space which is tangent o…

A Gaussian Process Ordinary Differential Equation framework for large continuous dynamical systems

A new method uses neural networks to improve POD-Galerkin models for complex systems.

We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three parts and we show how the integral curves of the original system can be reconstructe…

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space wh…

A mathematical model describes deforming manifolds with precise vectors and fields.

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where ba…

Automates PDE model reduction with time-scale separation.

Generative framework learns effective, lower-dimensional models from high-dimensional data.

We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equations is entirely based on the observation that the dynamics can be represented by a second-order differential equations vector field and th…

Develops an oblique projection technique to approximate a foliation for non-normal dynamics.

The paper analyzes variance reduction in stochastic gradient Langevin dynamics.

Unified product Lie groups and their quotient spaces are analyzed for dynamics.

iLED framework offers interpretable dynamics for multiscale systems.

This work learns models for population dynamics using variational methods and higher-order quadrature.

Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients evaluated on mini-batches are used as a replacement. In order to reduce the high vari…

A new geometric method approximates slow invariant manifolds without explicit time-scale separation.

Reduces complexity of financial contagion dynamics on networks.

New method finds efficient low-rank neural networks during training.

We investigate the statistical properties of the EBS order book for the EUR/USD and USD/JPY currency pairs and the impact of a ten-fold tick size reduction on its dynamics. A large fraction of limit orders are still placed right at or halfway between the old allowed prices. This generates price barriers where the best …

Abstract reviews symmetry and reduction in dynamical systems.

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features such as scale separation or symmetries, the time evolution of these variables typi…

The paper calculates sensitivities for financial derivatives using path weighting methods.

WeldNet reduces complex dynamics to simpler, manageable segments.

Develops a new model to predict training dynamics of large language models.

In this paper we consider an alternative approach to "un-reduction". This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential …

The stochastic knapsack has been used as a model in wide ranging applications from dynamic resource allocation to admission control in telecommunication. In recent years, a variation of the model has become a basic tool in studying problems that arise in revenue management and dynamic/flexible pricing; and it is in thi…

This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this trade-off is determined by one crucial design parameter. The main contribution is a methodology to app…

This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method combines the perspectives of model reduction and machine learning. Model reduction brin…

DGNet solves complex dynamical systems with neural networks and constraints.

New method learns low-dimensional models for systems with non-polynomial terms.

Balanced Neural ODEs combine VAEs and Neural ODEs for efficient time series modeling.

Survey of recent developments in symmetric reductions and controls for Hamiltonian systems.

We learn higher-order Markov random fields from evolving data, bypassing computational barriers.

Study on liquidity dynamics in Uniswap v3 pools using statistical methods.

Breaks down complex nonlinear dynamics into simpler components.

A model order reduction framework reduces financial risk analysis models efficiently.

Batch Thompson Sampling reduces exploration-exploitation trade-off in online decision making.

Paper tackles dynamic pricing in a geometrically decaying environment, achieving better occupancy with lower rates.

We propose an efficient protocol for decentralized training of deep neural networks from distributed data sources. The proposed protocol allows to handle different phases of model training equally well and to quickly adapt to concept drifts. This leads to a reduction of communication by an order of magnitude compared t…

Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide complete and accurate description of the…

This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dy…

Decentralized optimization on dynamic manifolds with improved regret bound.

Dynamic classifier chains with XGBoost reduces multi-label classification costs and improves label dependency handling.

A new DDR framework learns low-dimensional data representations using dynamical systems.

Efficiently simulates slow dynamics of high-dimensional stochastic systems.

Symmetry reduction of Painlevé IV to Flaschka-Newell Painlevé II