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In this study, we present a novel constraint-based algorithm for causal structure learning specifically designed for nonlinear autoregressive time series. Our algorithm significantly reduces computational complexity compared to existing…
Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics from limited data remains challenging. In this paper, we…
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…
Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed…
Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult…
In this paper we present a novel algorithm and efficient data structure for anomaly detection based on temporal data. Time-series data are represented by a sequence of symbolic time intervals, describing increasing and decreasing trends, in…
We present a representation learning algorithm that learns a low-dimensional latent dynamical system from high-dimensional \textit{sequential} raw data, e.g., video. The framework builds upon recent advances in amortized inference methods…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Algorithmic differentiation (AD) has become increasingly capable and straightforward to use. However, AD is inefficient when applied directly to solvers, a feature of most engineering analyses. We can leverage implicit differentiation to…
Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…
In one calculation, adjoint sensitivity analysis provides the gradient of a quantity of interest with respect to all system's parameters. Conventionally, adjoint solvers need to be implemented by differentiating computational models, which…
Model discovery based on existing data has been one of the major focuses of mathematical modelers for decades. Despite tremendous achievements of model identification from adequate data, how to unravel the models from limited data is less…
We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables…
Recent work has shown promising results in causal discovery by leveraging interventional data with gradient-based methods, even when the intervened variables are unknown. However, previous work assumes that the correspondence between…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
Traditional saliency map methods, popularized in computer vision, highlight individual points (pixels) of the input that contribute the most to the model's output. However, in time series, they offer limited insights, as semantically…
A method for nonlinear topology identification is proposed, based on the assumption that a collection of time series are generated in two steps: i) a vector autoregressive process in a latent space, and ii) a nonlinear, component-wise,…
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…