Related papers: CONFIDE: Contextual Finite Differences Modelling o…
Inference in current domains of application are often complex and require us to integrate the expertise of a variety of disparate panels of experts and models coherently. In this paper we develop a formal statistical methodology to guide…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often…
We study the problem of identifying unknown processes embedded in time-dependent partial differential equation (PDE) using observational data, with an application to advection-diffusion type PDE. We first conduct theoretical analysis and…
In this contribution, we augment the metric learning setting by introducing a parametric pseudo-distance, trained jointly with the encoder. Several interpretations are thus drawn for the learned distance-like model's output. We first show…
Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance. They additionally suffer from optimization…
Inference of fields defined in space and time from observational data is a core discipline in many scientific areas. This work approaches the problem in a Bayesian framework. The proposed method is based on statistically homogeneous random…
Latent stochastic differential equation (SDE) models are important tools for the unsupervised discovery of dynamical systems from data, with applications ranging from engineering to neuroscience. In these complex domains, exact posterior…
Observational data is increasingly used as a means for making individual-level causal predictions and intervention recommendations. The foremost challenge of causal inference from observational data is hidden confounding, whose presence…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…
The emergence of foundational models has significantly advanced segmentation approaches. However, challenges still remain in dense scenarios, where occlusions, scale variations, and clutter impede precise instance delineation. To address…
Deep learning models are widely used across computer vision and other domains. When working on the model induction, selecting the right architecture for a given dataset often relies on repetitive trial-and-error procedures. This procedure…
Estimation of causal effects is critical to a range of scientific disciplines. Existing methods for this task either require interventional data, knowledge about the ground truth causal graph, or rely on assumptions such as…
Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…
We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
Solving time-dependent parametric partial differential equations (PDEs) is challenging for data-driven methods, as these models must adapt to variations in parameters such as coefficients, forcing terms, and initial conditions.…
Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…