Related papers: Discovering the Unknowns: A First Step
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the…
Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform ${\Delta}$t between successive measurements); and at a specific time point only a subset of all variables may be sampled.…
Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…
As data-driven modeling of physical dynamical systems becomes more prevalent, a new challenge is emerging: making these models more compatible and aligned with existing human knowledge. AI-driven scientific modeling processes typically…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model…
An important and often overlooked aspect of particle filtering methods is the estimation of unknown static parameters. A simple approach for addressing this problem is to augment the unknown static parameters as auxiliary states that are…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…
Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…
Common workflows in machine learning and statistics rely on the ability to partition the information in a data set into independent portions. Recent work has shown that this may be possible even when conventional sample splitting is not…
This paper introduces a new technique for learning probabilistic models of mass and friction distributions of unknown objects, and performing robust sliding actions by using the learned models. The proposed method is executed in two…
Predictive models deployed in the real world may assign incorrect labels to instances with high confidence. Such errors or unknown unknowns are rooted in model incompleteness, and typically arise because of the mismatch between training…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…
In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…