Related papers: Model-Free Data-Driven Inference in Computational …
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
A crucial step in fitting a regression model to data is determining the model's structure, i.e., the subset of explanatory variables to be included. However, the uncertainty in this step is often overlooked due to a lack of satisfactory…
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used…
We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven…
The Model-free Prediction Principle has been successfully applied to general regression problems, as well as problems involving stationary and locally stationary time series. In this paper we demonstrate how Model-Free Prediction can be…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
Inverse design is a central goal in much of science and engineering, including frequency-selective surfaces (FSS) that are critical to microelectronics for telecommunications and optical metamaterials. Traditional surrogate-assisted…
In this paper, we establish an iterative data-driven approach to derive guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In this context, nonlinearity measures quantify the strength of the nonlinearity of a dynamical…
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…
When sample data are governed by an unknown sequence of independent but possibly non-identical distributions, the data-generating process (DGP) in general cannot be perfectly identified from the data. For making decisions facing such…
To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference…
The inferential model (IM) framework produces data-dependent, non-additive degrees of belief about the unknown parameter that are provably valid. The validity property guarantees, among other things, that inference procedures derived from…
Mathematical models are fundamental building blocks in the design of dynamical control systems. As control systems are becoming increasingly complex and networked, approaches for obtaining such models based on first principles reach their…
Whereas the ability of deep networks to produce useful predictions has been amply demonstrated, estimating the reliability of these predictions remains challenging. Sampling approaches such as MC-Dropout and Deep Ensembles have emerged as…
Physics-based simulations typically operate with a combination of complex differentiable equations and many scientific and geometric inputs. Our work involves gathering data from those simulations and seeing how well tree-based machine…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…
Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine information at different length scales. However, their application in a…
Machine learning has the potential to accelerate materials discovery by accurately predicting materials properties at a low computational cost. However, the model inputs remain a key stumbling block. Current methods typically use…
Gravitational-wave astronomy has entered a regime where it can extract information about the population properties of the observed binary black holes. The steep increase in the number of detections will offer deeper insights, but it will…