Loading...
Organizing Committee
University of Texas at Austin
Emory University
Sandia National Laboratories
Massachusetts Institute of Technology
Virginia Tech
The University of Chicago
Case Western Reserve University
Abstract
Inverse problems use experimental measurements to make inferences about parameters that describe mathematical models. The Bayesian approach to inverse problems models the unknown parameters as random variables and uses Bayes’ rule to combine the likelihood with the prior distribution to make inferences about the parameters. A major theme of this workshop is to develop new algorithms for UQ in Bayesian inverse problems which then has broad-ranging applications in many areas of science and engineering, such as medicine, security, geosciences, and materials science. A related area of interest to this program, known as data assimilation, also has similar goals but typically involves dynamical models. Also of interest are other areas such as sensitivity analysis, reduced order/surrogate modeling, experimental design, and extreme events.
The focus of this workshop is on probabilistic approaches for Bayesian inverse problems and uncertainty quantification. The workshop aims to bring together applied mathematics and statistics researchers from related, yet often disparate, fields of inverse problems, data assimilation, sensitivity analysis, experimental design, and uncertainty quantification, where stochastic methods are required for sampling (e.g., posterior distributions) but randomization can play a crucial role in mitigating computational costs.
The focus of this workshop is on probabilistic approaches for Bayesian inverse problems and uncertainty quantification. The workshop aims to bring together applied mathematics and statistics researchers from related, yet often disparate, fields of inverse problems, data assimilation, sensitivity analysis, experimental design, and uncertainty quantification, where stochastic methods are required for sampling (e.g., posterior distributions) but randomization can play a crucial role in mitigating computational costs.
Loading...
Loading participant list in background...
Workshop Schedule
Monday, March 02, 2026
8:50 - 9:00 AM EST
Welcome
11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
9:00 - 9:45 AM EST
Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting
11th Floor Lecture Hall
Speaker
Nikola Kovachki, NVIDIA Research
Session Chair
Julianne Chung, Emory University
Abstract
The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of forecast accuracy. Here, we demonstrate that state-of-the-art probabilistic skill requires neither intricate architectural constraints nor specialized training heuristics. We introduce a scalable framework for learning multi-scale atmospheric dynamics by combining a directly downsampled latent space with a history-conditioned local projector that resolves high-resolution physics. We find that our framework design is robust to the choice of probabilistic estimator, seamlessly supporting stochastic interpolants, diffusion models, and CRPS-based ensemble training. Validated against the Integrated Forecasting System and the deep learning probabilistic model GenCast, our framework achieves statistically significant improvements on most of the variables. These results suggest scaling a general-purpose model is sufficient for state-of-the-art medium-range prediction, eliminating the need for tailored training recipes and proving effective across the full spectrum of probabilistic frameworks."
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EST
Inverse Problems with Symmetry: A Functional Perspective on Multi-Reference Alignment
11th Floor Lecture Hall
Speaker
Anna Little, University of Utah
Session Chair
Julianne Chung, Emory University
Abstract
Motivated by biological imaging problems such as cryo-electron microscopy, multi-reference alignment (MRA) studies the recovery of a latent signal from noisy observations corrupted by unknown transformations. In this talk, I focus on recent work that formulates MRA directly in function space, removing restrictive discretization and bandlimited assumptions and revealing a new connection between functional MRA and classical deconvolution with replicated measurements. Leveraging a multivariate extension of Kotlarski’s identity, this approach enables explicit recovery of non-bandlimited signals from second-order statistics and yields sample-complexity guarantees that depend on interpretable parameters such as signal smoothness, noise variance, and correlation length scale. I will place these results in the context of earlier work on functional MRA under random dilations, where Fourier invariants can be systematically unbiased to accommodate non-compact group actions. Finally, I will outline ongoing work on functional multi-target detection, which extends MRA to regimes where multiple copies of a signal appear at unknown locations within a large, noisy observation.
11:30 AM - 12:15 PM EST
Efficient inverse problem solvers via randomized Krylov methods
11th Floor Lecture Hall
Speaker
Silvia Gazzola, University of Pisa
Session Chair
Julianne Chung, Emory University
Abstract
This talk is centered around two new efficient techniques that can be used to approximate (Tikhonov-like-)regularized solutions to large scale linear inverse problems, with an outlook on how such methods can be employed in a Bayesian setting.
First, we propose a randomized Golub-Kahan approach that builds on the recently developed randomized Gram-Schmidt process, where sketched inner products are used to estimate inner products of high-dimensional vectors. We describe new iterative solvers based on the randomized Golub-Kahan approach and show how they can be used for solving inverse problems with rectangular matrices, thus extending the capabilities of the recently proposed randomized GMRES method. We also consider hybrid projection methods that combine iterative projection methods, based on both the randomized Arnoldi and randomized Golub-Kahan factorizations, with Tikhonov regularization, where regularization parameters can be selected automatically during the iterative process.
Second, we consider the well-established FLSQR and FLSMR methods (i.e., flexible variants of LSQR and LSMR, respectively), which naturally allow modifications of the solution approximation subspace and/or handling inexact matrix-vector multiplications with the (transpose of the) coefficient matrix. We introduce sketched variants of FLSQR and FLSMR, where randomization becomes particularly effective, as it allows to recover short recurrences for the solution approximation.
Theoretical results are provided, and the performance of the new randomized Krylov methods is validated through numerical results in image deblurring, low-rank regularization and tomography with and without unmatched backprojectors.
12:30 - 2:30 PM EST
Lunch/Free Time
2:30 - 3:15 PM EST
Exploring intrinsic Gaussian processes as priors for inverse problems
11th Floor Lecture Hall
Speaker
David Higdon, Virgina Tech
Session Chair
Erkki Somersalo, Case Western Reserve University
Abstract
Stationary Gaussian processes (GPs) have long been a staple as priors for spatial fields to be inferred in a wide variety of inverse problems. GPs are proper distributions, defined by their mean and covariance functions. GPs have also proven remarkably extendable, leading to innovations such as deep GPs and Vecchia-based approximations for large systems. While the standard, stationary GP has an established track record, prominent researchers from the past (e.g. Matheron in the '70s, Besag in the '90s) have advocated intrinsic GPs in their stead. These intrinsic formulations are improper, and add some advantages, along with theoretical and computational hurdles. This talk will (re)introduce intrinsic GPs and explore how they might be used in Bayesian inverse problems and how resulting posteriors compare to stationary GP-based formulations. This is joint work with a number of colleagues at Virginia Tech.
3:30 - 4:00 PM EST
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EST
Almost nearly perfect Bayesian inversion with physics-informed deep generative models: Applications to computational imaging
11th Floor Lecture Hall
Speaker
Marcelo Pereyra, Heriot-Watt University
Session Chair
Erkki Somersalo, Case Western Reserve University
Abstract
This talk introduces a novel mathematical and computational framework for constructing high-dimensional Bayesian inversion methods that leverage state-of-the-art generative denoising diffusion models as highly informative priors. A central innovation is the use of Langevin diffusion processes and Markov chain Monte Carlo sampling techniques to create stochastic neural network architectures that perform nearly-perfect sampling. The obtained networks are modular and composed of interpretable layers that are directly related to statistical image priors and data likelihoods. The layers encoding the data likelihood function are designed for flexibility, enabling observation model parameters to be specified at inference time and seamlessly integrated with pre-trained foundational generative priors. To achieve high computational efficiency, we employ adversarial model distillation, which yields excellent sampling performance with as few as four Markov chain Monte Carlo steps, even in problems exceeding one million dimensions. Our approach is validated through non-asymptotic convergence analysis and extensive numerical experiments in computational image and video restoration. The talk is based on recent work in physics-informed generative AI for Bayesian imaging: https://arxiv.org/abs/2503.12615, which uses a distilled latent Stable Diffusion XL model trained on five billion clean images as a zero-shot prior; and https://arxiv.org/pdf/2507.02686, which integrates pixel-based diffusion models with deep unfolding and diffusion distillation.
5:00 - 6:30 PM EST
Reception
11th Floor Collaborative Space
Tuesday, March 03, 2026
9:00 - 9:45 AM EST
A unifying perspective of scientific machine learning with kernel methods
11th Floor Lecture Hall
Speaker
Bamdad Hosseini, University of Washington
Session Chair
Joseph Hart, Sandia National Laboratories
Abstract
In this talk I will discuss a general framework for unifying multiple problems in scientific machine learning (ML), in particular equation learning, PDE solvers, and operator learning. I will discuss how equation learning sits at the center of scientific ML and how it relates to classic ideas in control, inverse problems, and data assimilation. Then I will present an efficient kernel method that can learn equations and their solution maps implicitly. I will present some interesting numerical benchmarks as well as theoretical support in the form of convergence rates.
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EST
Preconditioned and iterative flow matching
11th Floor Lecture Hall
Speaker
Eldad Haber, The University of British Columbia
Session Chair
Joseph Hart, Sandia National Laboratories
Abstract
Flow matching and score-based diffusion train vector fields under intermediate distributions $p_t$, whose geometry can strongly affect their optimization. We show that the covariance $\Sigma_t$ of $p_t$ governs optimization bias: when
$\Sigma_t$ is ill-conditioned, gradient-based training rapidly fits high-variance directions while systematically under-optimizing low-variance modes, causing learning to plateau at suboptimal weights. We formalize this effect in analytically tractable settings and propose reversible, label-conditional \emph{preconditioning} maps that reshape the geometry of $p_t$ by improving the conditioning of $\Sigma_t$ without altering the underlying generative model. Rather than accelerating early convergence, preconditioning primarily mitigates optimization stagnation by enabling continued progress along previously suppressed directions. Across MNIST latent flow matching and \textcolor{red}{additional datasets}, we empirically track conditioning diagnostics, late-time errors, and distributional metrics, and show that preconditioning consistently yields better trained models by avoiding suboptimal plateaus.
11:30 AM - 12:15 PM EST
Leveraging predictive inverse problems to characterize uncertainties in the presence of model misspecification
11th Floor Lecture Hall
Speaker
Rebekah White, Sandia National Labs
Session Chair
Joseph Hart, Sandia National Laboratories
Abstract
For real-world engineering problems, computational models play a crucial role in informing predictions in extrapolative regimes where observational data may be unavailable, making meaningful uncertainty quantification essential. While Bayesian inference provides a unifying framework for characterizing and extrapolating uncertainties, standard approaches can underpredict uncertainties when model misspecification is present. Recently, frameworks for prediction-oriented inverse problems have aimed to remedy this shortcoming by directly targeting the predictive performance of inverse problem solutions. However, many open challenges and opportunities remain in applying these approaches to complex systems governed by differential equations, which are highlighted in this talk.
12:30 - 2:30 PM EST
Lunch/Free Time
2:30 - 3:15 PM EST
A Mixture-based Framework for Guiding Diffusion Models
11th Floor Lecture Hall
Speaker
Alain Durmus, Ecole Polytechnique
Session Chair
Tan Bui-Thanh, University of Texas at Austin
Abstract
Inverse problems—such as image restoration from noisy or incomplete measurements and musical source separation—are ill-posed, making Bayesian approaches with learned generative priors especially appealing. Diffusion models provide powerful priors, but existing posterior sampling methods often rely on crude likelihood-gradient approximations and heavy task-specific tuning. In this talk, I will introduce a novel principled approach specifically designed to overcome these limitations. The core contribution of this approach is the construction of a mixture approximation of intermediate posterior distributions defined by the diffusion model. The sampling is carried out sequentially via Gibbs sampling, a Markov Chain Monte Carlo method, using a careful data augmentation scheme. Gibbs sampling is employed here due to its simplicity and theoretical guarantees, allowing for exact conditional updates at each iteration, thus ensuring stability and efficiency. One key advantage of the presented algorithm is its flexibility: it adapts to varying levels of computational resources by adjusting the number of Gibbs iterations. Consequently, substantial performance gains can be achieved by increasing inference-time computational effort. I will present extensive experimental results demonstrating empirical performance across diverse image restoration tasks, involving both pixel-space and latent-space diffusion models, and showcase its successful application in musical source separation.
Joint work with Yazid Janati, Badr Moufad, Lisa Bedin, Alain Durmus, Randal Douc, Eric Moulines and Jimmy Olsson
3:30 - 4:00 PM EST
Coffee Break
11th Floor Collaborative Space
4:00 - 5:00 PM EST
Wednesday, March 04, 2026
9:00 - 9:45 AM EST
Separable Nonlinear Bayesian Inverse Problems
11th Floor Lecture Hall
Speaker
Malena Espanol, Arizona State University
Session Chair
Tan Bui-Thanh, University of Texas at Austin
Abstract
Separable nonlinear inverse problems arise in many applications where a forward model depends linearly on some unknowns and nonlinearly on others, including semi-blind deconvolution and kernel learning. In this talk, we adopt a Bayesian framework and assume Gaussian noise, along with Gaussian or other structured priors on the linear variables, as appropriate. We examine several prior models for the nonlinear parameters and show that these choices yield maximum a posteriori estimates formulated as solutions to regularized separable nonlinear least-squares problems that can be efficiently solved using the variable projection method. In addition, by marginalizing the linear variables, we obtain a reduced posterior over the nonlinear parameters that provides a Bayesian interpretation of variable projection, improves computational efficiency, and enables systematic uncertainty quantification in kernel learning. This is Joint work with Jordan Dworaczyk
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EST
Computationally efficient inference for sparsity-promoting hierarchical Bayesian models
11th Floor Lecture Hall
Speaker
Jan Glaubitz, Linköping University
Session Chair
Tan Bui-Thanh, University of Texas at Austin
Abstract
Hierarchical sparsity-promoting priors play a central role in Bayesian inverse problems, enabling adaptive regularization and uncertainty quantification for problems with sparse or piecewise-smooth unknowns. In particular, hierarchical sparsity-promoting scale-mixtures-of-normals models combine conditionally Gaussian priors with heavy-tailed hyperpriors, yielding flexible hierarchical formulations—but also posterior distributions that are high-dimensional, strongly correlated, and often multimodal, making efficient MCMC sampling challenging.
In this talk, I will present an approach to accelerate MCMC inference in hierarchical sparsity-promoting models via hierarchical prior normalization. The idea is to construct analytic transport maps that transform the full joint sparsity-promoting prior into a standard normal reference prior. I will further demonstrate how sampling the resulting prior-normalized posterior enables the use of efficient, structure-exploiting MCMC methods—such as elliptical slice sampling—and leads to improved mixing and robustness compared to conventional sampling from the original posterior, across a range of linear and nonlinear inverse problems
This talk is based on joint work with Youssef Marzouk (MIT) and Jonathan Lindbloom (Dartmouth College).
11:30 AM - 12:15 PM EST
Sparsity Promoting Scale Mixture Priors Fit Large Imaging Datasets
11th Floor Lecture Hall
Speaker
Alexander Strang, University of California Berkeley
Session Chair
Mirjeta Pasha, Virginia Tech
Abstract
Sparsity promoting priors have been widely proposed as the Bayesian extension of standard regularizers used for sparse inference. We study a family of hierarchical priors developed for sparse recovery in medical imaging. These are generalized-gamma scale mixtures of normals. This family has been proposed as an attractive alternative to standard sparsity promoting priors since it offers separate control over tail and peak behavior, so allows independent modeling of very small, and very large, entries, while only requiring two shape and one scale parameter. It includes all of the standard $\ell_p$ priors, as well as the Gaussian, Laplacian, and $t$ priors as special cases, though does not include priors that enforce an elastic-net or horshoe penalty. When applied to signals, it can represent Gaussian Process (GP) and $\alpha$-stable processes as special cases. It's hierarchical structure allows scalable inference and uncertainty quantification via coordinate blocking procedures. We provide the first large-scale empirical evidence that the prior family can fit a wide variety of image and audio datasets that vary by source, scale, and representation. We show that the prior provides accurate fits to speech recordings, remote sensing images of cities and agriculture, ice-bed topography, sea floor magnetic anomalies, surface air temperature maps, simulated brain MRI scans, and two large natural image datasets (COCO and SegmentAnything) under 7 different representations (Fourier, Gabor, Haar, AlexNet, Short-time Fourier, Continuous Wavelet, Erblet). The standard priors (e.g. GP priors) included as special cases fail to fit the majority of cases captured by the hierarchical prior. We contrast our results to a small set of images widely adopted as traditional benchmarks and explore signal features that cannot be described using the chosen prior.
12:25 - 12:30 PM EST
Group Photo (Immediately After Talk)
11th Floor Lecture Hall
12:30 - 2:30 PM EST
Lunch/Free Time
2:30 - 3:15 PM EST
Feature-to-feature mapping for complex physics
11th Floor Lecture Hall
Speaker
Roger Ghanem, University of Southern California
Session Chair
Youssef Marzouk, Massachusetts Institute of Technology
Abstract
I will describe recent developments to infer the dynamics of spatial features in a complex flow from observations of other related spatio-temporal features. We rely on accurate polynomial chaos constructions for both maps, predicated on the same input parameters, to frame the problem as one of conditional regression.
3:30 - 4:00 PM EST
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EST
Memorization and Regularization in Generative Diffusion Models
11th Floor Lecture Hall
Speaker
Ricardo Baptista, University of Toronto
Session Chair
Youssef Marzouk, Massachusetts Institute of Technology
Abstract
Diffusion models have emerged as a powerful framework for generative modeling in the information sciences and many scientific domains. To generate samples from the target distribution, these models rely on learning the the gradient of the data distribution's log-density using a score matching procedure. A key element for the success of diffusion models is that the optimal score function is not identified when solving the denoising score matching problem. In fact, the optimal score in both unconditioned and conditioned settings leads to a diffusion model that returns to the training samples and effectively memorizes the data distribution. In this presentation, we study the dynamical system associated with the optimal score and describe its long-term behavior relative to the training samples. Lastly, we show the effect of two forms of score function regularization on avoiding memorization: restricting the score's approximation space and early stopping of the training process. These results are numerically validated using distributions with and without densities including image-based inverse problems for scientific machine learning applications.
Thursday, March 05, 2026
9:00 - 9:45 AM EST
Fast Mixing MCMC without Gradients
11th Floor Lecture Hall
Speaker
Robert Scheichl, Heidelberg University
Session Chair
Andrea Arnold, Worcester Polytechnic Institute
Abstract
In this talk, I will revisit Multilevel Delayed Acceptance (MLDA) an efficient Markov chain Monte Carlo (MCMC) method for high-dimensional Bayesian inverse problems that does not require gradient information of the underlying posterior distribution. Instead, it uses a hierarchy of surrogates to accelerate convergence, e.g., coarser approximations of the likelihood. In previous works, we have demonstrated the fast convergence and the high effective sample size for MLDA, as well as multilevel variance reduction. In recent theoretical works, it has been shown that including gradient information allows to improve the upper bound on the total-variation mixing-time of MCMC from O(𝑑𝜅^2) for Random Walk Metropolis to O(𝑑𝜅) for MALA or O(𝑑^{11/12}𝜅) for HMC. Here, 𝜅 = 𝐿/𝑚 is the condition number of a 𝑚-strongly convex and 𝐿-smooth posterior distribution. We prove that for a suitable hierarchy of surrogates the same speedup as for MALA can be achieved by MLDA without explicit gradient evaluations. This requires two modifications of the surrogate densities in MLDA, akin to Tikhonov regularisation and tempering. Beyond these theoretical results, our numerical experiments indicate that successive states of the chain exhibit substantially reduced autocorrelation, even compared to the original MLDA. Numerical evidence suggests that incorporating tempering into the surrogate densities also improves robustness with respect to multimodality of the target density.
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EST
Multiproposal MCMC strategies under the large proposal limit perspective
11th Floor Lecture Hall
Speaker
Cecilia Mondaini, Drexel University
Session Chair
Andrea Arnold, Worcester Polytechnic Institute
Abstract
Multiproposal MCMC (MP-MCMC) algorithms generate clouds of proposals to efficiently explore the state space and uncover complex target geometries, while leveraging non-trivial parallel computing strategies that can lead to significant improvements over single proposal approaches. While several methods have been proposed involving a large number p of proposals within the MP-MCMC setting, much remains unknown about these algorithms, particularly in the large p-regime. In this talk, I will present on recent results where we propose new MP-MCMC algorithms under various types of proposal and acceptance structures, framed under a general state space multiproposal involutive theory we recently introduced. We rigorously obtain their large p-limit kernels, and also discover new relationships between different MP-MCMC methodologies, particularly ruling out certain existing approaches. This is a joint work with N. Glatt-Holtz (IU), A. Holbrook (UCLA), and J. Krometis (V Tech).
11:30 AM - 12:15 PM EST
Bayesian Weight Space Gaussian Process Regression in Practice
11th Floor Lecture Hall
Speaker
Habib Najm, Sandia National Laboratories
Session Chair
Andrea Arnold, Worcester Polytechnic Institute
Abstract
This talk will address various aspects of the application of Bayesian Gaussian process (GP) regression in model calibration. Focusing on the weight space view, I will outline GP utility for model calibration in the context of quantum chemical density functional theory. With this and other model problems, I will discuss matters of orthonormal basis choice and expansion order, and their impact on the solution. I will also discuss the a-posteriori application of constraints on the GP via projection, and will highlight the utilization of GPs for embedded model error estimation in physical models.
12:30 - 2:30 PM EST
Lunch/Free Time
2:30 - 3:15 PM EST
Exploiting low-dimensional structure in Bayesian inverse problems governed by complex models
11th Floor Lecture Hall
Speaker
Noemi Petra, University of California, Merced
Session Chair
Joseph Hart, Sandia National Laboratories
Abstract
Model-based projections of complex systems will play a central role in prediction and decision-making. However, models are typically subject to uncertainties stemming from uncertain inputs in the model such as coefficient fields, source terms, etc. Refining our understanding of such models requires solving a (Bayesian) inverse problem that integrates measurement data and the model to estimate and quantify the uncertainties in the parameters. Such problems face several challenges, e.g., high dimensionality of the inversion parameters, expensive to evaluate models, and various sources of uncertainties. In this talk, I will focus on identifying and exploiting low-dimensional structure in such inverse problems stemming for example from local sensitivity of the data with respect to parameters, diffusive models, sparse data, etc. The key idea is to exploit the fact that we can access second derivative information (via Hessian-applies which translate to PDE solves), an operator that often exhibits a low rank and even a lower off-diagonal structure. We can leverage this structure to build efficient preconditioners for the Newton-Krylov systems, to reduce the parameter and state dimensions, and to build fast-to-evaluate proposals in an MCMC context. We present numerical results for an inverse problem governed by an ice sheet flow model.
3:30 - 4:00 PM EST
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EST
Learning Disentangled Latent Spaces with Applications to Bayesian Inverse Problems
11th Floor Lecture Hall
Speaker
Emil Constantinescu, Argonne National Laboratory
Session Chair
Joseph Hart, Sandia National Laboratories
Abstract
Disentangled representations aim to learn latent coordinates that correspond to independent factors of variation in data. We present a framework that uses auxiliary-variable guidance to align selected latent dimensions with known physical quantities while allowing residual dimensions to capture remaining variability. This structured latent space can then be repurposed as a prior for Bayesian inverse problems: the deep generative model defines an implicit distribution over high-dimensional fields, and the disentangled coordinates provide an interpretable parameterization for inference. The resulting posteriors separate uncertainty over coarse physical parameters from fine-scale residual structure, enabling uncertainty quantification in domain-relevant terms. We discuss latent-space inference strategies and illustrate them in scientific applications.
Friday, March 06, 2026
9:00 - 9:45 AM EST
Optimal experimental design for inverse problems via column subset selection
11th Floor Lecture Hall
Speaker
Arvind Krishna Saibaba, North Carolina State University
Session Chair
Mirjeta Pasha, Virginia Tech
Abstract
Inverse problems require data to make inference about unknown parameters (typically spatial or spatiotemporal functions) of interest. However, only a limited amount of data can be collected, so it is imperative to collect data optimally to minimize the uncertainty associated with the unknown parameters. This talk will make new connections between to column subset selection, which is a well-studied problem in numerical linear algebra. This connection leads to several efficient algorithms, which are further accelerated by using randomization. The resulting algorithms are robust, computationally efficient, amenable to parallelization, require virtually no parameter tuning, and come with strong theoretical guarantees. Some of the proposed algorithms are also adjoint-free which is beneficial in situations, where the adjoint is expensive to evaluate or is not available. We demonstrate the performance of the algorithms on model problems involving partial differential equations and tomography.
10:00 - 10:45 AM EST
Solving and Learning Partial Differential Equations with Q-Exponential Processes
11th Floor Lecture Hall
Speaker
Shiwei Lan, Arizona State University
Session Chair
Mirjeta Pasha, Virginia Tech
Abstract
Solving and learning partial differential equations (PDEs) lies at the core of physics-informed machine learning. Traditional numerical methods, such as finite difference and finite element approaches, are rooted in domain-specific techniques and often lack scalability. Recent advances have introduced neural networks and Gaussian processes (GPs) as flexible tools for automating PDE solving and incorporating physical knowledge into learning frameworks. While GPs offer tractable predictive distributions and a principled probabilistic foundation, they may be suboptimal in capturing complex behaviors such as sharp transitions or non-smooth dynamics. To address this limitation, we propose the use of the $q$-exponential process (Q-EP), a recently developed generalization of GPs designed to better handle data with abrupt changes and to more accurately model derivative information. We advocate for Q-EP as a superior alternative to GPs in solving PDEs and associated inverse problems. Leveraging sparse variational inference, our method enables principled uncertainty quantification -- a capability not naturally afforded by neural network-based approaches. Through a series of experiments, including the Eikonal equation, Burgers’ equation, and an inverse Darcy flow problem, we demonstrate that the variational Q-EP method consistently yields more accurate solutions while providing meaningful uncertainty estimates.
11:00 - 11:30 AM EST
Coffee Break
11th Floor Collaborative Space
11:30 AM - 12:15 PM EST
New frontiers for hierarchical Bayesian models in inverse problems
11th Floor Lecture Hall
Speaker
Daniela Calvetti, Case Western Reserve University
Session Chair
Mirjeta Pasha, Virginia Tech
Abstract
This talk will discuss how to bring together hierarchical Bayesian techniques in inverse problems with novel ideas leveraging data science techniques and state of the art methods to address large scale computing challenges arising in a number of important real world applications. In particular, we will focus on dictionary learning methods applied to inverse problems, design of informative dictionaries and sparsity promoting techniques.
Request Reimbursement
This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.
- ORCID iD
- As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
- Acceptable Costs
- 1 roundtrip between your home institute and ICERM
- Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
- Ground Transportation to and from airports and ICERM.
- Unacceptable Costs
- Flights on non-U.S. or non-E.U. airlines
- Flights on U.K. airlines
- Seats in economy plus, business class, or first class
- Change ticket fees of any kind
- Multi-use bus passes
- Meals or incidentals
- Advance Approval Required
- Personal car travel to ICERM from outside New England
- Multiple-destination plane ticket; does not include layovers to reach ICERM
- Arriving or departing from ICERM more than a day before or day after the program
- Multiple trips to ICERM
- Rental car to/from ICERM
- Flights on a Swiss, Japanese, or Australian airline
- Arriving or departing from airport other than PVD/BOS or home institution’s local airport
- 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
- Travel Maximum Contributions
- New England: $350
- Other contiguous US: $850
- Asia & Oceania: $2,000
- All other locations: $1,500
- Note these rates were updated in Spring 2023 and supersede any prior invitation rates.
- Reimbursement Requests
Request Reimbursement with Cube
Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.
- Reimbursement Tips
- Scanned original receipts are required for all expenses
- Airfare receipt must show full itinerary and payment
- ICERM does not offer per diem or meal reimbursement
- Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via Google Maps PDF
- Keep all documentation until you receive your reimbursement!
- Reimbursement Timing
6–8 weeks after all documentation is sent to ICERM. All reimbursements are reviewed by multiple Brown University offices.
- Reimbursement Deadline
Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. No submissions are accepted after six months.
