arXiv research

BayTiDe discovers time-delayed differential equations from noisy data.

Study on synchronization in financial markets with time delays.

In this paper we investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in finance when we want to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending…

Improved GRU model with weighted time-delay feedback for long-term dependencies.

In this paper we consider backward stochastic differential equations with time-delayed generators of a moving average type. The classical framework with linear generators depending on $(Y(t),Z(t))$ is extended and we investigate linear generators depending on $(\frac{1}{t}\int_0^tY(s)ds, \frac{1}{t}\int_0^tZ(s)ds)$. We…

We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation that introduces feedback in the dynamics and eliminates the necessity of interm…

Improved modeling of chaotic systems using time-delay embeddings and Frenet-Serret frame.

Proposes neural delay differential equations for stable system identification with partially observed states.

TSMB handles time delays in multivariate time series data.

In this paper we studied about the wavelet identification of the thresholds and time delay for more general case without the constraint that the time delay is smaller than the order of the model. Here we composed an empirical wavelet from the SETAR (Self-Exciting Threshold Autoregressive) model and identified the thres…

New method estimates traffic congestion delays using statistical causality.

This paper provides a mathematical framework for time-delay reservoir computing.

In this paper we show that several dynamical systems with time delay can be described as vector fields associated to smooth functions via a bracket of Leibniz structure. Some examples illustrate the theoretical considerations.

Time-delayed embeddings avoid self-intersections for high enough delay.

Predicting conversion rates (CVRs) in display advertising (e.g., predicting the proportion of users who purchase an item (i.e., a conversion) after its corresponding ad is clicked) is important when measuring the effects of ads shown to users and to understanding the interests of the users. There is generally a time de…

This paper presents a stochastic logic time delay reservoir design. The reservoir is analyzed using a number of metrics, such as kernel quality, generalization rank, performance on simple benchmarks, and is also compared to a deterministic design. A novel re-seeding method is introduced to reduce the adverse effects of…

Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a…

Measures time-delay embedding for noisy, sparse data.

Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a…

Survey of RL methods for control systems with time delays.

New method disentangles latent variables in nonstationary data.

ERDMD discovers sparse, nonuniformly timed DMD models from chaotic attractors.

Latency (i.e., time delay) in electronic markets affects the efficacy of liquidity taking strategies. During the time liquidity takers process information and send marketable limit orders (MLOs) to the exchange, the limit order book (LOB) might undergo updates, so there is no guarantee that MLOs are filled. We develop …

In this paper we study the problem of convergence and generalization error bound of stochastic momentum for deep learning from the perspective of regularization. To do so, we first interpret momentum as solving an $\ell_2$-regularized minimization problem to learn the offsets between arbitrary two successive model para…

TreeDOX predicts chaotic systems without hyperparameter tuning.

Neural Laplace Control tackles offline RL for continuous-time delayed systems with irregular observations.

Algorithm improves RL by discovering delayed causal relations.

In this paper we present a continuous time dynamical model of heterogeneous agents interacting in a financial market where transactions are cleared by a market maker. The market is composed of fundamentalist, trend following and contrarian agents who process information from the market with different time delays. Each …

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity…

The Backpropagation algorithm relies on the abstraction of using a neural model that gets rid of the notion of time, since the input is mapped instantaneously to the output. In this paper, we claim that this abstraction of ignoring time, along with the abrupt input changes that occur when feeding the training set, are …

We consider the static and dynamic models of Cournot duopoly with tax evasion. In the dynamic model we introduce the time delay and we analyze the local stability of the stationary state. There is a critical value of the delay when the Hopf bifurcation occurs.

Studies projective geometry and partial differential equations prolongation.

Paper solves a class of differential equations with specific solutions.

The paper generalizes Monge-Ampère equations and their solutions in differential geometry.

We propose a novel {\it Equilibrated Recurrent Neural Network} (ERNN) to combat the issues of inaccuracy and instability in conventional RNNs. Drawing upon the concept of autapse in neuroscience, we propose augmenting an RNN with a time-delayed self-feedback loop. Our sole purpose is to modify the dynamics of each inte…

DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and differential equations. We demonstrate the ability to incorporate DifferentialEqua…

Classifies scalar second-order PDEs with low-dimensional symmetry groups.

Neural differential equations combine deep learning and differential equations for modeling complex systems.

Neural networks can approximate complex stochastic equations well.

This paper considers an often forgotten relationship, the time delay between a cause and its effect in economies and finance. We treat the case of Foreign Direct Investment (FDI) and economic growth, - measured through a country Gross Domestic Product (GDP). The pertinent data refers to 43 countries, over 1970-2015, - …

New method solves PDEs for any initial condition without retraining.

Paper discovers governing equations from data using differential invariants.

We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly …

Framework LiLY recovers latent causal variables from time-series data under distribution shifts.

A reliable controller is critical and essential for the execution of safe and smooth maneuvers of an autonomous vehicle.The controller must be robust to external disturbances, such as road surface, weather, and wind conditions, and so on.It also needs to deal with the internal parametric variations of vehicle sub-syste…

New variational principle found for non-variational differential equations.

In this paper we propose a novel observer-based method to improve the safety and security of connected and automated vehicle (CAV) transportation. The proposed method combines model-based signal filtering and anomaly detection methods. Specifically, we use adaptive extended Kalman filter (AEKF) to smooth sensor reading…

Developed a theory of local convexity for second order differential equations on Lie algebroids.