Invited Talk at SIAM MDS26: Learning Filtering Distributions Using Strictly Proper Scoring Rules

Tue, 14 Jul 2026 00:00:00 +0000

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I am pleased to share that I will give an invited talk at the in Salt Lake City this November.

My talk, “Learning Filtering Distributions Using Strictly Proper Scoring Rules,” will be part of the minisymposium

Structure-Preserving Data Assimilation and Learning for Complex Dynamical Systems — Part I of III

organized by Tongtong Li (University of Maryland, Baltimore County) and Lizuo Liu (Dartmouth College). I am grateful to the organizers for the invitation and look forward to the discussion.

Talk at a Glance

Talk: Learning Filtering Distributions Using Strictly Proper Scoring Rules
Minisymposium: Structure-Preserving Data Assimilation and Learning for Complex Dynamical Systems — Part I of III
Conference: SIAM Conference on Mathematics of Data Science (MDS26)
Conference dates: November 16–20, 2026
Venue: Salt Palace Convention Center, Salt Lake City, Utah, U.S.
Session date, time, and room: To be announced in the official program

The detailed session assignment has not yet appeared on the . I will update this post when SIAM publishes the schedule.

About the Talk

Bayesian filtering seeks the evolving conditional distribution of a hidden dynamical state given partial and noisy observations. This distribution is the natural object for uncertainty quantification, especially when nonlinear dynamics or observations lead to non-Gaussian and multimodal posteriors. Yet the true filtering distribution is generally intractable and therefore unavailable as a supervised learning target.

In this talk, I will present the proper scoring ensemble filter (PSEF), which learns an ensemble analysis map using simulated state–observation trajectories. The central idea is to train with a strictly proper scoring rule—the energy score in our implementation—so that the expected objective is uniquely optimized by the full filtering distribution rather than only its conditional mean.

Our analysis map is a permutation-invariant transformer that takes a forecast ensemble and the latest observation as input and returns an analysis ensemble. Under a realizability assumption, we show that the population objective recovers the Bayesian filtering distribution. Numerical experiments demonstrate accurate filtering for nonlinear and non-Gaussian systems, including multimodal posteriors that are missed by classical Gaussian filters and learning methods based on mean-squared error.

This is joint work with Eviatar Bach, Ricardo Baptista, Jochen Bröcker, and Andrew Stuart.

Paper:
Code:
Publication page and BibTeX:
Research announcement:

Minisymposium Theme

The three-part minisymposium brings together researchers working on structure-preserving data assimilation, inverse problems, uncertainty quantification, feature-aware learning, and scientific machine learning. Its focus is on methods that incorporate knowledge of the underlying dynamics—such as physical constraints, coherent structures, and informative representations—to improve the stability, robustness, interpretability, and predictive performance of learning and inference in nonlinear and multiscale systems.

I look forward to presenting this work and to seeing many of you in Salt Lake City!

Organizing ‘Measure Transport for Inverse Problems and Data Assimilation’ at SIAM MDS26

Mon, 18 May 2026 00:00:00 +0000

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Overview

I am pleased to share that , , and I will be organizing a minisymposium titled

Measure Transport for Inverse Problems and Data Assimilation

at the .

Minisymposium Abstract

Inverse problems and data assimilation require efficient characterization of posterior distributions from indirect and noisy observations, often in high-dimensional or function-space settings. Measure transport methods provide a powerful alternative to traditional sampling approaches by constructing maps that push forward simple reference measures to posterior distributions, enabling efficient sampling and amortized inference.

This minisymposium brings together recent developments in transport-based methodologies, spanning ideas from transport maps and ensemble Kalman methods to modern generative modeling approaches and operator-based formulations. Despite their different formulations, these approaches share a common perspective: casting inference as the pushforward of measures.

The session will highlight theoretical advances and computational methods, with the goal of clarifying connections between these approaches and identifying new directions for scalable uncertainty quantification.

Conference Details

Conference: SIAM Conference on Mathematics of Data Science (MDS26)
Dates: November 16–20, 2026
Location: Salt Palace Convention Center, Salt Lake City, Utah, U.S.
Format: Fully in person; remote and prerecorded presentations are not permitted
Conference hashtag: #SIAMMDS26

MDS26 will be held jointly with the and the .

Minisymposium Schedule

Update (July 14, 2026): SIAM has not yet posted the detailed MDS26 schedule or speaker index. The minisymposium’s session number, date, time, room, speakers, and talk titles are therefore still to be announced. SIAM states that these details will be published in July 2026 on the official . I will update this post when the session assignment becomes available.

SIAM’s standard format for a minisymposium is four 25-minute presentations, with five additional minutes for discussion after each talk. A minisymposium may have up to three parts and twelve speakers.

Key Dates

April 20, 2026: Minisymposium proposal submission deadline
May 18, 2026: Minisymposium presentation abstract submission deadline
July 2026: Conference schedule and speaker index expected
August 17, 2026: Travel support application deadline
October 19, 2026: Early registration and hotel reservation deadlines
November 16–20, 2026: SIAM MDS26 in Salt Lake City

We hope to see many of you in Salt Lake City!

SIAM MDS26 | Bohan Chen's Personal Webpage