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Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient continuous-time way to model functions of potentially…
A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose…
An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and…
Differential evolution (DE) is an effective global evolutionary optimization algorithm using to solve global optimization problems mainly in a continuous domain. In this field, researchers pay more attention to improving the capability of…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex…
Data-enabled predictive control (DeePC) has garnered significant attention for its ability to achieve safe, data-driven optimal control without relying on explicit system models. Traditional DeePC methods use pre-collected input/output…
Multivariate time series(MTS) is a universal data type related to many practical applications. However, MTS suffers from missing data problems, which leads to degradation or even collapse of the downstream tasks, such as prediction and…
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
Modeling real-world multidimensional time series can be particularly challenging when these are sporadically observed (i.e., sampling is irregular both in time and across dimensions)-such as in the case of clinical patient data. To address…
A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…
Deep learning inspired by differential equations is a recent research trend and has marked the state of the art performance for many machine learning tasks. Among them, time-series modeling with neural controlled differential equations…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
Functional evolution equations are used in the modeling of numerous physical processes. In this work, our main tool is perturbation theory of strongly continuous semigroups. The advantage of this technique is that one can provide functional…
This paper addresses the problem of cooperative target tracking using a heterogeneous multi-robot system, where the robots are communicating over a dynamic communication network, and heterogeneity is in terms of different types of sensors…
Delay differential equations (DDEs) are widely used in mathematical modeling to describe physical and biological systems. Delays can impact model dynamics, resulting in oscillatory behavior. In physiological systems, this instability may…
Nonlinear PDEs give rise to complex dynamics that are often difficult to analyze in state space due to their relatively large numbers of degrees of freedom, ill-conditioned operators, and changing spatial and parameter resolution…
We consider delay differential algebraic equations (DDAEs) to model interconnected systems with time-delays. The DDAE framework does not require any elimination techniques and can directly deal with any interconnection of systems and…