arXiv research

Improves inverse uncertainty quantification for time-dependent data using PCA and deep neural networks.

Surrogate models help predict complex systems with less computational cost.

We solve the dynamics of large spherical Minority Games (MG) in the presence of non-negligible time dependent external contributions to the overall market bid. The latter represent the actions of market regulators, or other major natural or political events that impact on the market. In contrast to non-spherical MGs, t…

Proposes a Koopman operator method for time-dependent reliability analysis of nonlinear systems.

DeepONet accelerates reliability analysis of stochastic nonlinear systems.

This work develops fast and accurate ROMs for AM models using OL methods.

In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and "shape". We show t…

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of dimensionality, the saturation discontinuity due to capillarity effects, and the time-depende…

Machine learning offers novel ways and means to design personalized learning systems wherein each student's educational experience is customized in real time depending on their background, learning goals, and performance to date. SPARse Factor Analysis (SPARFA) is a novel framework for machine learning-based learning a…

CoNBONet improves reliability analysis of complex systems with fast, energy-efficient predictions.

Estimates conditional distribution function using neural networks for censored and uncensored data.

Study examines how industrial emissions evolve over time in response to various factors.

Study of time-dependent metrics and connections in geometry.

We present an analysis of the price impact associated with trades effected by different financial firms. Using data from the Spanish Stock Market, we find a high degree of heterogeneity across different market members, both in the instantaneous impact functions and in the time-dependent market response to trades by ind…

In many applications, observed data are influenced by some combination of latent causes. For example, suppose sensors are placed inside a building to record responses such as temperature, humidity, power consumption and noise levels. These random, observed responses are typically affected by many unobserved, latent fac…

In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.

Study on relativistic nonholonomic mechanics with time-dependent constraints.

The aim of this paper is to geometrize time dependent Lagrangian mechanics in a way that the framework of second order tangent bundles plays an essential role. To this end, we first introduce the concepts of time dependent connections and time dependent semisprays on a manifold $M$ and their induced vector bundle struc…

Proposes a method to estimate time-dependent probability density functions using binary classifiers.

In this article we get a time-dependent Sobolev inequality along the Ricci flow which generalizes the earlier results of Zhang, Ye, Hsu. As an application of the time-dependent Sobolev inequality, we also get a growth of the ratio of bob-collapsing along the Ricci flow.

Paper adapts causal analysis for time-dependent systems, especially energy management.

Model predicts COVID-19 growth in Senegal, highlighting health care capacity importance.

The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered trees on the basis of their subpaths, which are vertical substructures of trees resp…

The aim of this paper is to obtain on the dual 1-jet space J^{1*}(R;M) the main geometrical objects used in the dual jet geometry of time-dependent Hamiltonians. We talk about distinguished (d-) tensors, time-dependent semisprays, nonlinear connections and their mathematical connections.

The paper extends Marsden-Weinstein reduction to mechanical presymplectic structures for time-dependent Hamiltonian systems.

In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems. In particular, we generalize the cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and corresponding Jacobi's last multiplier for 3D systems. We illustrate our cons…

Proposes a method to predict responses from covariates over time.

Flexible Cox model for time-dependent covariates with complex sparsity patterns.

We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The …

Paper shows how scattering maps of Schrödinger equations relate to metrics.

The usual formulation of time-dependent mechanics implies a given splitting $Y=R\times M$ of an event space $Y$. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The goal is the frame-covariant formulation of time-dependent mechanics on a bundle…

Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type equations with time dependent parameters and give the general symmetry structure of th…

In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …

A new RNN model tackles long-time dependencies with fast, invertible, and memory-efficient hidden states.

SurvSHAP(t) explains time-dependent survival predictions from machine learning models.

In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration…

Develops semi-closed form solutions for barrier and American options on time-dependent OU process.

DynForest R package predicts outcomes with time-dependent predictors.

The usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a splitting is broken under reference frame transformations and time-dependent canonical …

Path integral method calculates PDBS option prices with time-dependent parameters.

The paper analyzes time-dependent streaming data with biased gradient estimates and proposes improved stochastic optimization methods.

Based on our previous study [IS3] on the stationary scattering theory for the Schrodinger operator on a manifold possessing an escape function we complete our investigation by doing the time-dependent counterpart. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends, possibly with unbounde…

We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying space as a super Ricci flow as previously introduced by the second author. Our ma…

This work presents an exact solution to the generalized Heston model, where the model parameters are assumed to have linear time dependence The solution for the model in expressed in terms of confluent hypergeometric functions.

The paper analyzes convergence of Langevin dynamics with time-dependent metrics.

We analyze families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e., a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study…

Develops methods to learn correlation potentials for time-dependent Kohn-Sham systems.

Paper develops semi-analytic method for American options in time-dependent jump-diffusion models.