arXiv subjects

Julie Bessac

Publications and source records attributed to Julie Bessac.

At least 19 recordsLinked to original sources

arXiv2026

Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks

Linear dimensionality reduction methods such as proper orthogonal decomposition (POD) make high-dimensional data amenable to analysis by identifying the principal components, or modes, that capture the most variance, or energy, in the data and constructing a low-dimensional representation in the subspace they span. Such linear methods struggle, however, for data with slowly decaying Kolmogorov $n$-widths, such as advection-dominated and turbulent flows, which require many modes for accurate reconstruction; moreover, energy-based truncation can discard low-energy modes needed to capture small-scale features. Recent nonlinear manifold methods using polynomial mappings with alternating or greedy mode selection achieve better reconstruction with fewer modes, but fix the form of the nonlinear mapping a priori, limiting expressivity. In contrast, neural network (NN) manifolds offer greater expressivity yet employ energy-based selection. We present SparseModesNet, a dimensionality reduction framework that employs linear encoding and nonlinear NN decoding. The decoder leverages LassoNet, a method enforcing hierarchical sparsity through a residual connection with a linear skip layer, to simultaneously select informative modes and learn a nonlinear mapping that minimizes reconstruction error. On benchmark advection-dominated and chaotic flows, SparseModesNet matches or exceeds state-of-the-art performance. For turbulent channel flow at friction Reynolds number $Re_\tau = 5200$, our method reduces reconstruction error by 51-78% compared to existing polynomial manifold methods while maintaining interpretability through physically meaningful mode selection.

physics.flu-dyn↗

arXiv2026

Uncovering Physical Drivers of Dark Matter Halo Structures with Auxiliary-Variable-Guided Generative Models

Deep generative models (DGMs) compress high-dimensional data but often entangle distinct physical factors in their latent spaces. We present an auxiliary-variable-guided framework for disentangling representations of thermal Sunyaev-Zel'dovich (tSZ) maps of dark matter halos. We introduce halo mass and concentration as auxiliary variables and apply a lightweight alignment penalty to encourage latent dimensions to reflect these physical quantities. To generate sharp and realistic samples, we extend latent conditional flow matching (LCFM), a state-of-the-art generative model, to enforce disentanglement in the latent space. Our Disentangled Latent-CFM (DL-CFM) model recovers the established mass-concentration scaling relation and identifies latent space outliers that may correspond to unusual halo formation histories. By linking latent coordinates to interpretable astrophysical properties, our method transforms the latent space into a diagnostic tool for cosmological structure. This work demonstrates that auxiliary guidance preserves generative flexibility while yielding physically meaningful, disentangled embeddings, providing a generalizable pathway for uncovering independent factors in complex astronomical datasets.

stat.ML↗

arXiv2026

Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systems

Projection-based model reduction enables efficient simulation of complex dynamical systems by constructing low-dimensional surrogate models from high-dimensional data. The Operator Inference (OpInf) approach learns such reduced surrogate models through a two-step process: constructing a low-dimensional basis via Singular Value Decomposition (SVD) to compress the data, then solving a linear least-squares (LS) problem to infer reduced operators that govern the dynamics in this compressed space, all without access to the underlying code or full model operators, i.e., non-intrusively. Traditional OpInf operates as a batch learning method, where both the SVD and LS steps process all data simultaneously. This poses a barrier to deployment of the approach on large-scale applications where dataset sizes prevent the loading of all data into memory at once. Additionally, the traditional batch approach does not naturally allow model updates using new data acquired during online computation. To address these limitations, we propose Streaming OpInf, which learns reduced models from sequentially arriving data streams. Our approach employs incremental SVD for adaptive basis construction and recursive LS for streaming operator updates, eliminating the need to store complete data sets while enabling online model adaptation. The approach can flexibly combine different choices of streaming algorithms for numerical linear algebra: we systematically explore the impact of these choices both analytically and numerically to identify effective combinations for accurate reduced model learning. Numerical experiments on benchmark problems and a large-scale turbulent channel flow demonstrate that Streaming OpInf achieves accuracy comparable to batch OpInf while reducing memory requirements by over 99% and enabling dimension reductions exceeding 31,000x, resulting in orders-of-magnitude faster predictions.

math.NA↗

arXiv2025

Multi-modal Bayesian Neural Network Surrogates with Conjugate Last-Layer Estimation

As data collection and simulation capabilities advance, multi-modal learning, the task of learning from multiple modalities and sources of data, is becoming an increasingly important area of research. Surrogate models that learn from data of multiple auxiliary modalities to support the modeling of a highly expensive quantity of interest have the potential to aid outer loop applications such as optimization, inverse problems, or sensitivity analyses when multi-modal data are available. We develop two multi-modal Bayesian neural network surrogate models and leverage conditionally conjugate distributions in the last layer to estimate model parameters using stochastic variational inference (SVI). We provide a method to perform this conjugate SVI estimation in the presence of partially missing observations. We demonstrate improved prediction accuracy and uncertainty quantification compared to uni-modal surrogate models for both scalar and time series data.

stat.ML↗

arXiv2025

Multidimensional Distributional Neural Network Output Demonstrated in Super-Resolution of Surface Wind Speed

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic uncertainty, few offer closed-form, multidimensional distributions that preserve spatial correlation while remaining computationally tractable. In this work, we present a framework for training neural networks with a multidimensional Gaussian loss, generating closed-form predictive distributions over outputs with non-identically distributed and heteroscedastic structure. Our approach captures aleatoric uncertainty by iteratively estimating the means and covariance matrices, and is demonstrated on a super-resolution example. We leverage a Fourier representation of the covariance matrix to stabilize network training and preserve spatial correlation. We introduce a novel regularization strategy -- referred to as information sharing -- that interpolates between image-specific and global covariance estimates, enabling convergence of the super-resolution downscaling network trained on image-specific distributional loss functions. This framework allows for efficient sampling, explicit correlation modeling, and extensions to more complex distribution families all without disrupting prediction performance. We demonstrate the method on a surface wind speed downscaling task and discuss its broader applicability to uncertainty-aware prediction in scientific models.

cs.LG↗

arXiv2025

Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction

Quadratic manifolds for nonintrusive reduced modeling are typically trained to minimize the reconstruction error on snapshot data, which means that the error of models fitted to the embedded data in downstream learning steps is ignored. In contrast, we propose a greedy training procedure that takes into account both the reconstruction error on the snapshot data and the prediction error of reduced models fitted to the data. Because our procedure learns quadratic manifolds with the objective of achieving accurate reduced models, it avoids oscillatory and other non-smooth embeddings that can hinder learning accurate reduced models. Numerical experiments on transport and turbulent flow problems show that quadratic manifolds trained with the proposed greedy approach lead to reduced models with up to two orders of magnitude higher accuracy than quadratic manifolds trained with respect to the reconstruction error alone.

math.DS↗

arXiv2025

Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets

This study addresses the challenge of statistically extracting generative factors from complex, high-dimensional datasets in unsupervised or semi-supervised settings. We investigate encoder-decoder-based generative models for nonlinear dimensionality reduction, focusing on disentangling low-dimensional latent variables corresponding to independent physical factors. Introducing Aux-VAE, a novel architecture within the classical Variational Autoencoder framework, we achieve disentanglement with minimal modifications to the standard VAE loss function by leveraging prior statistical knowledge through auxiliary variables. These variables guide the shaping of the latent space by aligning latent factors with learned auxiliary variables. We validate the efficacy of Aux-VAE through comparative assessments on multiple datasets, including astronomical simulations.

stat.ML↗

arXiv2025

Summary Statistics of Large-scale Model Outputs for Observation-corrected Outputs

Physics-based models capture broad spatial and temporal dynamics, but often suffer from biases and numerical approximations, while observations capture localized variability but are sparse. Integrating these complementary data modalities is important to improving the accuracy and reliability of model outputs. Meanwhile, physics-based models typically generate large outputs that are challenging to manipulate. In this paper, we propose Sig-PCA, a space-time framework that integrates summary statistics from model outputs with localized observations via a neural network (NN). By leveraging reduced-order representations from physics-based models and integrating them with observational data, our approach corrects model outputs, while allowing to work with dimensionally-reduced quantities hence with smaller NNs. This framework highlights the synergy between observational data and statistical summaries of model outputs, and effectively combines multisource data by preserving essential statistical information. We demonstrate our approach on two datasets (surface temperature and surface wind) with different statistical properties and different ratios of model to observational data. Our method corrects model outputs to align closely with the observational data, specifically enabling to correct probability distributions and space-time correlation structures.

stat.ME↗

arXiv2025

A copula-based rank histogram ensemble filter

Serial ensemble filters implement triangular probability transport maps to reduce high-dimensional inference problems to sequences of state-by-state univariate inference problems. The univariate inference problems are solved by sampling posterior probability densities obtained by combining constructed prior densities with observational likelihoods according to Bayes' rule. Many serial filters in the literature focus on representing the marginal posterior densities of each state. However, rigorously capturing the conditional dependencies between the different univariate inferences is crucial to correctly sampling multidimensional posteriors. This work proposes a new serial ensemble filter, called the copula rank histogram filter (CoRHF), that seeks to capture the conditional dependency structure between variables via empirical copula estimates; these estimates are used to rigorously implement the triangular (state-by-state univariate) Bayesian inference. The success of the CoRHF is demonstrated on two-dimensional examples and the Lorenz '63 problem. A practical extension to the high-dimensional setting is developed by localizing the empirical copula estimation, and is demonstrated on the Lorenz '96 problem.

stat.ME↗

arXiv2024

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

This work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in-situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

math.NA↗

arXiv2024

Constructing Level Sets Using Smoothed Approximate Bayesian Computation

This paper presents a novel approach to level set estimation for any function/simulation with an arbitrary number of continuous inputs and arbitrary numbers of continuous responses. We present a method that uses existing data from computer model simulations to fit a Gaussian process surrogate and use a newly proposed Markov Chain Monte Carlo technique, which we refer to as Smoothed Approximate Bayesian Computation to sample sets of parameters that yield a desired response, which improves on ``hard-clipped" versions of ABC. We prove that our method converges to the correct distribution (i.e. the posterior distribution of level sets, or probability contours) and give results of our method on known functions and a dam breach simulation where the relationship between input parameters and responses of interest is unknown. Two versions of S-ABC are offered based on: 1) surrogating an accurately known target model and 2) surrogating an approximate model, which leads to uncertainty in estimating the level sets. In addition, we show how our method can be extended to multiple responses with an accompanying example. As demonstrated, S-ABC is able to estimate a level set accurately without the use of a predefined grid or signed distance function.

stat.ME↗

arXiv2024

A Framework for Balancing Power Grid Efficiency and Risk with Bi-objective Stochastic Integer Optimization

Power grid expansion planning requires making large investment decisions in the present that will impact the future cost and reliability of a system exposed to wide-ranging uncertainties. Extreme temperatures can pose significant challenges to providing power by increasing demand and decreasing supply and have contributed to recent major power outages. We propose to address a modeling challenge of such high-impact, low-frequency events with a bi-objective stochastic integer optimization model that finds solutions with different trade-offs between efficiency in normal conditions and risk to extreme events. We propose a conditional sampling approach paired with a risk measure to address the inherent challenge in approximating the risk of low-frequency events within a sampling based approach. We present a model for spatially correlated, county-specific temperatures and a method to generate both unconditional and conditionally extreme temperature samples from this model efficiently. These models are investigated within an extensive case study with realistic data that demonstrates the effectiveness of the bi-objective approach and the conditional sampling technique. We find that spatial correlations in the temperature samples are essential to finding good solutions and that modeling generator temperature dependence is an important consideration for finding efficient, low-risk solutions.

math.OC↗

arXiv2023

Modeling spatial asymmetries in teleconnected extreme temperatures

Combining strengths from deep learning and extreme value theory can help describe complex relationships between variables where extreme events have significant impacts (e.g., environmental or financial applications). Neural networks learn complicated nonlinear relationships from large datasets under limited parametric assumptions. By definition, the number of occurrences of extreme events is small, which limits the ability of the data-hungry, nonparametric neural network to describe rare events. Inspired by recent extreme cold winter weather events in North America caused by atmospheric blocking, we examine several probabilistic generative models for the entire multivariate probability distribution of daily boreal winter surface air temperature. We propose metrics to measure spatial asymmetries, such as long-range anticorrelated patterns that commonly appear in temperature fields during blocking events. Compared to vine copulas, the statistical standard for multivariate copula modeling, deep learning methods show improved ability to reproduce complicated asymmetries in the spatial distribution of ERA5 temperature reanalysis, including the spatial extent of in-sample extreme events.

stat.AP↗

arXiv2023

Black-Box Statistical Prediction of Lossy Compression Ratios for Scientific Data

Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless compression, no theoretical or data-based quantification of lossy compressibility exists for scientific data. Users rely on trial and error to assess lossy compression performance. As a strong data-driven effort toward quantifying lossy compressibility of scientific datasets, we provide a statistical framework to predict compression ratios of lossy compressors. Our method is a two-step framework where (i) compressor-agnostic predictors are computed and (ii) statistical prediction models relying on these predictors are trained on observed compression ratios. Proposed predictors exploit spatial correlations and notions of entropy and lossyness via the quantized entropy. We study 8+ compressors on 6 scientific datasets and achieve a median percentage prediction error less than 12%, which is substantially smaller than that of other methods while achieving at least a 8.8x speedup for searching for a specific compression ratio and 7.8x speedup for determining the best compressor out of a collection.

cs.DC↗

arXiv2022

Statistical treatment of convolutional neural network super-resolution of inland surface wind for subgrid-scale variability quantification

Machine learning models have been employed to perform either physics-free data-driven or hybrid dynamical downscaling of climate data. Most of these implementations operate over relatively small downscaling factors because of the challenge of recovering fine-scale information from coarse data. This limits their compatibility with many global climate model outputs, often available between $\sim$50--100 km resolution, to scales of interest such as cloud resolving or urban scales. This study systematically examines the capability of convolutional neural networks (CNNs) to downscale surface wind speed data over land surface from different coarse resolutions (25 km, 48 km, and 100 km resolution) to 3 km. For each downscaling factor, we consider three CNN configurations that generate super-resolved predictions of fine-scale wind speed, which take between 1 to 3 input fields: coarse wind speed, fine-scale topography, and diurnal cycle. In addition to fine-scale wind speeds, probability density function parameters are generated, through which sample wind speeds can be generated accounting for the intrinsic stochasticity of wind speed. For generalizability assessment, CNN models are tested on regions with different topography and climate that are unseen during training. The evaluation of super-resolved predictions focuses on subgrid-scale variability and the recovery of extremes. Models with coarse wind and fine topography as inputs exhibit the best performance compared with other model configurations, operating across the same downscaling factor. Our diurnal cycle encoding results in lower out-of-sample generalizability compared with other input configurations.

physics.ao-ph↗

arXiv2022

Joint modeling of wind speed and wind direction through a conditional approach

Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. In this work we develop a conditional approach to model these two variables, where the joint distribution is decomposed into the product of the marginal distribution of wind direction and the conditional distribution of wind speed given wind direction. To accommodate the circular nature of wind direction a von Mises mixture model is used; the conditional wind speed distribution is modeled as a directional dependent Weibull distribution via a two-stage estimation procedure, consisting of a directional binned Weibull parameter estimation, followed by a harmonic regression to estimate the dependence of the Weibull parameters on wind direction. A Monte Carlo simulation study indicates that our method outperforms an alternative method that uses periodic spline quantile regression in terms of estimation efficiency. We illustrate our method by using the output from a regional climate model to investigate how the joint distribution of wind speed and direction may change under some future climate scenarios.

stat.AP↗

arXiv2022

Station-wise statistical joint assessment of wind speed and direction under future climates across the United States

This study develops a statistical conditional approach to evaluate climate model performance in wind speed and direction and to project their future changes under the representative concentration pathway 8.5 scenario over inland and offshore locations across the Continental United States. The proposed conditional approach extends the scope of existing studies by characterizing the changes of the full range of the joint wind speed and direction distribution. Directional wind speed distributions are estimated using two statistical methods: a Weibull distributional regression model and a quantile regression model, both of which enforce the circular constraint to their resulting estimates of directional distributions. Projected uncertainties associated with different climate models and model internal variability are investigated and compared with the climate change signal to quantify the statistical significance of the future projections. In particular this work extends the concept of internal variability to the standard deviation and high quantiles to assess the relative magnitudes to their projected changes. The evaluation results show that the studied climate model capture both historical wind speed, wind direction, and their dependencies reasonably well over both inland and offshore locations. In the future, most of the locations show no significant changes in mean wind speeds in both winter and summer, although the changes in standard deviation and 95th-quantile show some robust changes over certain locations in winter. The proposed conditional approach enables the characterization of the directional wind speed distributions, which offers additional insights for the joint assessment of speed and direction.

stat.AP↗

arXiv2021

Exploring Lossy Compressibility through Statistical Correlations of Scientific Datasets

Lossy compression plays a growing role in scientific simulations where the cost of storing their output data can span terabytes. Using error bounded lossy compression reduces the amount of storage for each simulation; however, there is no known bound for the upper limit on lossy compressibility. Correlation structures in the data, choice of compressor and error bound are factors allowing larger compression ratios and improved quality metrics. Analyzing these three factors provides one direction towards quantifying lossy compressibility. As a first step, we explore statistical methods to characterize the correlation structures present in the data and their relationships, through functional models, to compression ratios. We observed a relationship between compression ratios and statistics summarizing correlation structure of the data, which are a first step towards evaluating the theoretical limits of lossy compressibility used to eventually predict compression performance and adapt compressors to correlation structures present in the data.

stat.AP↗