Proposes a Koopman operator method for time-dependent reliability analysis of nonlinear systems.
problem Challenges in time-dependent reliability analysis of nonlinear dynamical systems.
method Koopman operator approach for transforming nonlinear systems into linear ones, combined with deep learning for intrinsic coordinates.
result Robust and generalizable approach for time-dependent reliability analysis, superior to purely data-driven methods.
MAntRA combines machine learning and Bayesian methods for time-dependent reliability analysis of unknown systems.
problem Time-dependent reliability analysis of systems with unknown governing physics.
method Combines machine learning, Bayesian statistics, and stochastic integration to discover and analyze SDEs from data.
result Demonstrates the effectiveness of MAntRA on three numerical examples, indicating its potential for in-situ and heritage structure analysis.
DeepONet accelerates reliability analysis of stochastic nonlinear systems.
problem Time-dependent reliability analysis of systems with stochastic forcing.
method DeepONet, a novel operator network, learns function-to-function mappings.
result DeepONet efficiently and accurately predicts system responses.
CoNBONet improves reliability analysis of complex systems with fast, energy-efficient predictions.
problem Time-dependent reliability analysis of nonlinear systems under stochastic excitations is computationally demanding.
method CoNBONet combines deep operator networks with neuroscience-inspired neuron models for fast, energy-efficient inference.
result CoNBONet provides reliable coverage of failure probabilities with theoretical guarantees.
Economics tool predicts failure times in reliability systems.
problem Predicting optimal failure times in weighted k-out-of-n reliability systems with heterogeneous component failure.
method Using rational expectations to analyze and predict failure times in reliability systems with heterogeneous component failure.
result Different measures are optimal for predicting system failure depending on component failure distributions.
Proposes a method to estimate time-dependent probability density functions using binary classifiers.
problem Estimating time-dependent probability density functions of stochastic processes.
method Trains a time-dependent binary classifier to discriminate between realizations of a stochastic process at two nearby time instants.
result Explicitly models and accurately reconstructs complex time-dependent, multi-modal, and near-degenerate densities.
Robust feature-weighted jump models for time-dependent clustering
problem Temporal clustering
method Robust feature-weighted jump model
result Accurate recovery of true cluster sequence and feature identification
New method models longitudinal data using variational inference and normalizing flows.
problem Handling high-dimensional longitudinal data with time dependency.
method Variational inference with normalizing flows for latent variables.
result The method achieves better likelihood estimates and more reliable missing data imputation.
We review the main "omnibus procedures" for goodness-of-fit testing for copulas: tests based on the empirical copula process, on probability integral transformations, on Kendall's dependence function, etc, and some corresponding reductions of dimension techniques. The problems of finding asymptotic distribution-free te…
Study of time-dependent metrics and connections in geometry.
problem Understanding geodesics and connections in time-dependent Riemannian manifolds.
method Examine connections on product manifolds, explore parallel transport, geodesics, and torsion.
result Define the derivative of a one-parameter family of connections.
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.
problem Formulating classical time-dependent nonholonomic mechanics.
method Invariant formulation using moving frames and Chaplygin systems.
result Hamiltonization of time-dependent constraints achieved.
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…
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.
problem Challenges in root-cause analysis for systems with lagged time-dependencies, particularly in energy management.
method Adapts causal root-cause analysis method to time-dependent systems, discusses two truncation approaches.
result Extension effectively localizes root-causes in feature and time domain with enough lags.
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.
Adaptive time decay functions improve financial product recommendation accuracy.
problem Inaccurate recommendations due to static historical data in finance.
method Time-dependent collaborative filtering with personalized decay functions.
result Significant improvements over state-of-the-art benchmarks in financial product recommendation.
The paper extends Marsden-Weinstein reduction to mechanical presymplectic structures for time-dependent Hamiltonian systems.
problem Limitations of Marsden-Weinstein reduction for cosymplectic structures in time-dependent Hamiltonian systems.
method Developed Marsden-Weinstein reduction for mechanical presymplectic structures.
result Mechanical presymplectic structures provide a more suitable framework for time-dependent Hamiltonian systems than cosymplectic structures.
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…
Flexible Cox model for time-dependent covariates with complex sparsity patterns.
problem Lack of flexibility in enforcing specific sparsity patterns in time-dependent Cox models.
method Proposes a flexible framework for variable selection in time-dependent Cox models, accommodating complex selection rules.
result Achieves accurate estimation with low false alarm rates for complex covariate structures.
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.
problem Relating scattering maps of time-dependent Schrödinger equations to metrics.
method Analyzes scattering maps for specific classes of metrics and diffeomorphisms.
result Scattering maps differ by a compact operator if and only if metrics are related by diffeomorphism.
The usual formulation of time-dependent mechanics implies a given splitting Y=R×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.
problem Challenges in processing sequential inputs with long-time dependencies in RNNs.
method A novel RNN architecture based on a Hamiltonian system of oscillators.
result The proposed RNN mitigates exploding and vanishing gradient problems, providing state-of-the-art performance.
SurvSHAP(t) explains time-dependent survival predictions from machine learning models.
problem Interpreting complex survival models for time-dependent effects.
method SHapley Additive exPlanations (SHAP) adapted for time-dependent survival predictions.
result SurvSHAP(t) detects time-dependent effects and improves variable importance detection.
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…
Paper presents a method to reduce prediction variance of DNNs for unknown systems.
problem Uncertainty in DNN predictions due to high variance.
method Ensemble averaging of multiple DNN models trained independently.
result Reduction in variance of DNN predictions, improving reliability.
Develops semi-closed form solutions for barrier and American options on time-dependent OU process.
problem Valuation of barrier and American options on a time-dependent Ornstein-Uhlenbeck process.
method Semi-closed form solutions involving numerical solution of Fredholm equations and integration of Jacobi theta functions.
result Method is more efficient than backward finite difference method and can be as efficient as forward finite difference solver with better accuracy and stability.
DynForest R package predicts outcomes with time-dependent predictors.
problem Handling time-dependent predictors in random forest models.
method Random forests with time-dependent predictors summarized using flexible linear mixed models.
result DynForest can predict continuous, categorical, and survival outcomes.
The usual formulations of time-dependent mechanics start from a given splitting Y=R×M of the coordinate bundle Y→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.
problem Pricing proportional double-barrier step options with time-dependent interest rates and volatilities.
method Path integral method applied to a quantum mechanical analogy of barrier options.
result Derivation of pricing kernel for PDBS options with time-dependent parameters.
The paper analyzes time-dependent streaming data with biased gradient estimates and proposes improved stochastic optimization methods.
problem Stochastic optimization in a streaming setting with time-dependent and biased gradient estimates.
method Analysis of several first-order methods including SGD, mini-batch SGD, and time-varying mini-batch SGD, along with their Polyak-Ruppert averages.
result Time-varying mini-batch SGD methods can break long- and short-range dependence structures, and biased SGD methods can achieve comparable performance to their unbiased counterparts.
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.
problem Analyzing convergence of Langevin dynamics with time-dependent metrics.
method Formulated a modified gradient flow of the Kullback-Leibler divergence, selected a time-dependent relative Fisher information functional, and developed a time-dependent Hessian matrix condition.
result Proved convergence conditions for various Langevin dynamics.
Temporal Normalizing Flows enhance density estimation of time-dependent data.
problem Accurate and robust density estimation of time-dependent stochastic data.
method Leveraging normalizing flows for temporal data, tNFs estimate multi-scale distributions without prior scale knowledge.
result Temporal Normalizing Flows improve density estimation of time-dependent data, including multi-scale distributions.
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.
problem Learning the correlation potential for time-dependent Kohn-Sham systems.
method Optimizing a least-squares objective subject to the TDKS equation using adjoints.
result Learned correlation potential models match ground truth electron densities and can have memory.
Paper develops semi-analytic method for American options in time-dependent jump-diffusion models.
problem Pricing American options in models with time-dependent and exponential jumps.
method Generalizes existing methods for barrier and American options to handle arbitrary time dependencies and solves the problem through algebraic and Fredholm-Volterra equations.
result Presents a semi-analytic solution for American options in time-dependent jump-diffusion models with exponential jumps.
The paper proposes a time-dependent Markov model for a limit order book.
problem Understanding the convergence of a limit order book to a more complex diffusion.
method A simple time-dependent Markov model is proposed, describing the arrival of different orders.
result Empirical studies verify the validity of the modeling assumptions for certain stocks.
A new framework predicts links in time-dependent networks using Bernoulli autoregression.
problem Predicting links in time-dependent networks with additional auxiliary information.
method A Bernoulli autoregressive model with regularization for link discovery.
result The model can discover new links not present in the data.
ParaRNN improves RNN interpretability and parallelizability for time-dependent data.
problem Limited interpretability and slow training of RNNs.
method Parallelized RNN with additive representation and recurrence features.
result ParaRNN achieves comparable performance to vanilla RNNs but with improved interpretability and efficiency.
A new Bayesian method optimizes time-dependent expensive functions with lookahead.
problem Maximizing a time-dependent, expensive oracle with limited evaluations.
method Recursive, two-step lookahead expected payoff (r2LEY) acquisition function.
result r2LEY outperforms myopic methods in synthetic and real-world datasets.
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…
Study heat flow on changing surfaces, proving existence and uniqueness.
problem Existence and uniqueness of heat flow on time-varying manifolds.
method Establishes estimates for heat flow under minimal assumptions, focusing on logarithmic derivative of volume measure.
result Proves estimates hold for Ricci flow with scalar curvature bounded below, dependent only on initial data.