arXiv subjects

Donatella Pasqualini

Publications and source records attributed to Donatella Pasqualini.

7 recordsLinked to original sources

arXiv2026

Supervised Learning of Functional Outcomes with Predictors at Different Scales: A Functional Gaussian Process Approach

The analysis of complex computer simulations, often involving functional data, presents unique statistical challenges. Conventional regression methods, such as function-on-function regression, typically associate functional outcomes with both scalar and functional predictors on a per-realization basis. However, simulation studies often demand a more nuanced approach to disentangle nonlinear relationships of functional outcome with predictors observed at multiple scales: domain-specific functional predictors that are fixed across simulation runs, and realization-specific global predictors that vary between runs. In this article, we develop a novel supervised learning framework tailored to this setting. We propose an additive nonlinear regression model that flexibly captures the influence of both predictor types. The effects of functional predictors are modeled through spatially-varying coefficients governed by a Gaussian process prior. Crucially, to capture the impact of global predictors on the functional outcome, we introduce a functional Gaussian process (fGP) prior. This new prior jointly models the entire collection of unknown, spatially-indexed nonlinear functions that encode the effects of the global predictors over the entire domain, explicitly accounting for their spatial dependence. This integrated architecture enables simultaneous learning from both predictor types, provides a principled strategies to quantify their respective contributions in predicting the functional outcome, and delivers rigorous uncertainty estimates for both model parameters and predictions. The utility and robustness of our approach are demonstrated through multiple synthetic datasets and a real-world application involving outputs from the Sea, Lake, and Overland Surges from Hurricanes (SLOSH) model.

stat.ME↗

arXiv2025

Interpretable Deep Neural Network for Modeling Functional Surrogates

Developing surrogates for computer models has become increasingly important for addressing complex problems in science and engineering. This article introduces an artificial intelligent (AI) surrogate, referred to as the DeepSurrogate, for analyzing functional outputs with vector-valued inputs. The relationship between the functional output and vector-valued input is modeled as an infinite sequence of unknown functions, each representing the relationship at a specific location within the functional domain. These spatially indexed functions are expressed through a combination of basis functions and their corresponding coefficient functions, both of which are modeled using deep neural networks (DNN). The proposed framework accounts for spatial dependencies across locations, while capturing the relationship between the functional output and scalar predictors. It also integrates a Monte Carlo (MC) dropout strategy to quantify prediction uncertainty, enhancing explainability in the deep neural network architecture. The proposed method enables efficient inference on datasets with approximately 50,000 spatial locations and 20 simulations, achieving results in under 10 minutes using standard hardware. The approach is validated on extensive synthetic datasets and a large-scale simulation from the Sea Lake and Overland Surge from Hurricanes (SLOSH) simulator. An open-source Python package implementing the method is made available.

stat.ME↗

arXiv2024

Robust Distributed Learning of Functional Data From Simulators through Data Sketching

In environmental studies, realistic simulations are essential for understanding complex systems. Statistical emulation with Gaussian processes (GPs) in functional data models have become a standard tool for this purpose. Traditional centralized processing of such models requires substantial computational and storage resources, leading to emerging distributed Bayesian learning algorithms that partition data into shards for distributed computations. However, concerns about the sensitivity of distributed inference to shard selection arise. Instead of using data shards, our approach employs multiple random matrices to create random linear projections, or sketches, of the dataset. Posterior inference on functional data models is conducted using random data sketches on various machines in parallel. These individual inferences are combined across machines at a central server. The aggregation of inference across random matrices makes our approach resilient to the selection of data sketches, resulting in robust distributed Bayesian learning. An important advantage is its ability to maintain the privacy of sampling units, as random sketches prevent the recovery of raw data. We highlight the significance of our approach through simulation examples and showcase the performance of our approach as an emulator using surrogates of the Sea, Lake, and Overland Surges from Hurricanes (SLOSH) simulator - an important simulator for government agencies.

stat.AP↗

arXiv2020

Exact Mixed-integer Convex Programming Formulation for Optimal Water Network Design

In this paper, we consider the canonical water network design problem, which contains nonconvex potential loss functions and discrete resistance choices with varying costs. Traditionally, to resolve the nonconvexities of this problem, relaxations of the potential loss constraints have been applied to yield a more tractable mixed-integer convex program (MICP). However, design solutions to these relaxed problems may not be feasible with respect to the full nonconvex physics. In this paper, it is shown that, in fact, the original mixed-integer nonconvex program can be reformulated exactly as an MICP. Beginning with a convex program previously used for proving nonlinear network design feasibility, strong duality is invoked to construct a novel, convex primal-dual system embedding all physical constraints. This convex system is then augmented to form an exact MICP formulation of the original design problem. Using this novel MICP as a foundation, a global optimization algorithm is developed, leveraging heuristics, outer approximations, and feasibility cutting planes for infeasible designs. Finally, the algorithm is compared against the previous relaxation-based state of the art in water network design over a number of standard benchmark instances from the literature.

math.OC↗

arXiv2019

The ISTI Rapid Response on Exploring Cloud Computing 2018

This report describes eighteen projects that explored how commercial cloud computing services can be utilized for scientific computation at national laboratories. These demonstrations ranged from deploying proprietary software in a cloud environment to leveraging established cloud-based analytics workflows for processing scientific datasets. By and large, the projects were successful and collectively they suggest that cloud computing can be a valuable computational resource for scientific computation at national laboratories.

cs.DC↗

arXiv2006

Nonequilibrium and Nonlinear Dynamics in Geomaterials I : The Low Strain Regime

Members of a wide class of geomaterials are known to display complex and fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range of bulk strains, down to surprisingly low values, e.g., 10^{-7}. In this paper we investigate two sandstones, Berea and Fontainebleau, and characterize their behavior under the influence of very small external forces via carefully controlled resonant bar experiments. By reducing environmental effects due to temperature and humidity variations, we are able to systematically and reproducibly study dynamical behavior at strains as low as 10^{-9}. Our study establishes the existence of two strain thresholds, the first, epsilon_L, below which the material is essentially linear, and the second, epsilon_M, below which the material is nonlinear but where quasiequilibrium thermodynamics still applies as evidenced by the success of Landau theory and a simple macroscopic description based on the Duffing oscillator. At strains above epsilon_M the behavior becomes truly nonequilibrium -- as demonstrated by the existence of material conditioning -- and Landau theory no longer applies. The main focus of this paper is the study of the region below the second threshold, but we also comment on how our work clarifies and resolves previous experimental conflicts, as well as suggest new directions of research.

cond-mat.mtrl-sci↗

arXiv2004

Nonlinear and Nonequilibrium Dynamics in Geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.

cond-mat.mtrl-sci↗