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06/28/2023
The curse of dimensionality in operator learning
Neural operator architectures employ neural networks to approximate oper...
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06/21/2023
Learning Homogenization for Elliptic Operators
Multiscale partial differential equations (PDEs) arise in various applic...
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04/26/2023
The Nonlocal Neural Operator: Universal Approximation
Neural operator architectures approximate operators between infinite-dim...
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09/23/2022
Ensemble Kalman Methods: A Mean Field Perspective
This paper provides a unifying mean field based framework for the deriva...
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08/09/2022
Second Order Ensemble Langevin Method for Sampling and Inverse Problems
We propose a sampling method based on an ensemble approximation of secon...
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05/27/2022
Learning Markovian Homogenized Models in Viscoelasticity
Fully resolving dynamics of materials with rapidly-varying features invo...
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04/09/2022
Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems
We consider Bayesian inference for large scale inverse problems, where c...
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03/24/2022
The Cost-Accuracy Trade-Off In Operator Learning With Neural Networks
The term `surrogate modeling' in computational science and engineering r...
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01/12/2022
Ensemble-Based Experimental Design for Targeted High-Resolution Simulations to Inform Climate Models
Targeted high-resolution simulations driven by a general circulation mod...
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08/27/2021
Convergence Rates for Learning Linear Operators from Noisy Data
We study the Bayesian inverse problem of learning a linear operator on a...
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07/14/2021
A Framework for Machine Learning of Model Error in Dynamical Systems
The development of data-informed predictive models for dynamical systems...
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04/07/2021
Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods
The increasing availability of data presents an opportunity to calibrate...
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02/02/2021
Unscented Kalman Inversion
A useful approach to solve inverse problems is to pair the parameter-to-...
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12/24/2020
Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM
Parameters in climate models are usually calibrated manually, exploiting...
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09/28/2020
Drift Estimation of Multiscale Diffusions Based on Filtered Data
We study the problem of drift estimation for two-scale continuous time s...
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07/25/2020
Posterior Consistency of Semi-Supervised Regression on Graphs
Graph-based semi-supervised regression (SSR) is the problem of estimatin...
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05/20/2020
The Random Feature Model for Input-Output Maps between Banach Spaces
Well known to the machine learning community, the random feature model, ...
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05/07/2020
Model Reduction and Neural Networks for Parametric PDEs
We develop a general framework for data-driven approximation of input-ou...
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04/17/2020
Learning Stochastic Closures Using Ensemble Kalman Inversion
Although the governing equations of many systems, when derived from firs...
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01/10/2020
Calibrate, Emulate, Sample
Many parameter estimation problems arising in applications are best cast...
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09/13/2019
Spectral Analysis Of Weighted Laplacians Arising In Data Clustering
Graph Laplacians computed from weighted adjacency matrices are widely us...
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06/18/2019
Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods
Graph-based semi-supervised learning is the problem of propagating label...
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06/10/2019
Analysis Of Momentum Methods
Gradient decent-based optimization methods underpin the parameter traini...
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05/10/2019
Hyperparameter Estimation in Bayesian MAP Estimation: Parameterizations and Consistency
The Bayesian formulation of inverse problems is attractive for three pri...
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05/10/2019
Inverse optimal transport
Discrete optimal transportation problems arise in various contexts in en...
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10/15/2018
Inverse Problems and Data Assimilation
These notes are designed with the aim of providing a clear and concise i...
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08/10/2018
Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks
The standard probabilistic perspective on machine learning gives rise to...
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05/23/2018
Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms
Scalings in which the graph Laplacian approaches a differential operator...
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03/09/2018
Robust MCMC Sampling with Non-Gaussian and Hierarchical Priors in High Dimensions
A key problem in inference for high dimensional unknowns is the design o...
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11/30/2017
How Deep Are Deep Gaussian Processes?
Recent research has shown the potential utility of probability distribut...
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03/26/2017