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Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior,…
Although deep-learning has been successfully applied in a variety of science and engineering problems owing to its strong high-dimensional nonlinear mapping capability, it is of limited use in scientific knowledge discovery. In this work,…
Smoothed model checking based on Gaussian process classification provides a powerful approach for statistical model checking of parametric continuous time Markov chain models. The method constructs a model for the functional dependence of…
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…
We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations.…
We propose an adaptive numerical solver for the study of viscoelastic 2D two-phase flows using the volume-of-fluid method. The scheme uses the robust log conformation tensor technique of Fattal & Kupferman (2004,2005} combined with the…
The paper is devoted to homogenization of two-phase incompressible viscoelastic flows with disordered microstructure. We study two cases. In the first case, both phases are modeled as Kelvin-Voight viscoelastic materials. In the second…
Simulating particle dynamics with high fidelity is crucial for solving real-world interaction and control tasks involving liquids in design, graphics, and robotics. Recently, data-driven approaches, particularly those based on graph neural…
In this paper, a new efficient and generalized consistency correction method for weakly-compressible smoothed particle hydrodynamics is proposed and successfully implemented in the simulation of violent free-surface flow exhibiting breaking…
Recent advancements in data-driven aeroelasticity have been driven by the wealth of data available in the wind engineering practice, especially in modeling aerodynamic forces. Despite progress, challenges persist in addressing free-stream…
With the recent development of new geometric and angular-radial frameworks for multivariate extremes, reliably simulating from angular variables in moderate-to-high dimensions is of increasing importance. Empirical approaches have the…
Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an…
Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…
The smoothed particle hydrodynamics (SPH) method has been increasingly used to study fluid problems in recent years; but its computational cost can be high if high resolution is required. In this study, an adaptive resolution method based…
Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…
Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…
Biological soft tissues exhibit substantial inter-subject variability, making the automation of constitutive material modeling essential for patient-specific analysis and design. Such materials are not only highly nonlinear but also display…
Retinal prostheses restore vision by electrically stimulating surviving neurons, but calibrating perceptual thresholds (i.e., the minimum stimulus intensity required for perception) remains a time-intensive challenge, especially for…
Accurate kinematic models are essential for effective control of surgical robots. For tendon driven robots, which is common for minimally invasive surgery, intrinsic nonlinearities are important to consider. Traditional analytical methods…
Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…