Bath Numerical Analysis Seminar

Fridays at 12.15 at Wolfson 4W 1.7. All talks will be broadcast on Zoom.

Link to Zoom meeting

Everyone is welcome at these talks.

Date	Speaker	Title
2 Oct 2026	NA+DS Group Members	NA+DS Research Meeting (staff only)
9 Oct 2026	Takeshi Koshizuka (RIKEN Center for Advanced Intelligence Project)	Connecting Distributions via Schrödinger Bridges: Which Path, and How to Learn It Transporting one probability distribution to another is a fundamental problem arising in population dynamics inference, generative modeling, and sampling from energy functions. Since infinitely many paths can connect two distributions, two essential questions arise: which path should we choose, and how can we learn it stably? This talk addresses both questions through the variational principles underlying optimal transport (OT) and Schrödinger bridges (SB). In the first part, we start from Monge-Kantorovich OT and move to its Benamou-Brenier dynamic formulation. We then extend the transport cost to general Lagrangian costs, leading naturally to the Lagrangian Schrödinger bridge framework. We show how incorporating physical structure into the Lagrangian can select plausible transport paths, and introduce our Neural Lagrangian Schrödinger Bridge method. In the second part, we revisit SB from a path-space optimization perspective. Viewing SB as a KL projection provides a unified interpretation of Sinkhorn and iterative proportional fitting (IPF) as alternating KL projections, and connects IPF to mirror descent. Building on this perspective, we introduce a Trust-Region Schrödinger Bridge Sampler for targets specified only through an energy function. By adaptively controlling the mirror-descent step size through a trust-region constraint, the method mitigates mode collapse and training instability in existing approaches.
16 Oct 2026	Sam McCallum (University of Bath)	Strong Stochastic Flow Maps Flow and diffusion models generate high-quality samples in many modalities; however, many network evaluations are required during inference due to numerical integration of an underlying differential equation. Flow maps alleviate this problem by learning the solution map of the differential equation directly. Yet, current methods are restricted to approximating the solution map of ODEs. In this talk, we introduce a framework for learning the strong solution map of SDEs, termed Strong Stochastic Flow Maps. We apply this method to learn the solution map of diffusion models, allowing for few-step stochastic sampling. We additionally present some new work extending the method to Langevin dynamics and show that this can enable large-timestep molecular dynamics simulations.
23 Oct 2026	Eviatar Bach (University of Reading)	Learning Probabilistic Filters for Data Assimilation (joint 'NA+DS+Stats' seminar, so will start at 1:15pm) Filtering, the problem of estimating the probability distribution of a system’s states given partial and noisy observations, is essential for weather forecasting, along with other areas of science and engineering. Obtaining the filtering distribution is generally intractable for high-dimensional, nonlinear systems. The ensemble Kalman filter (EnKF) approximates the filtering distribution with an ensemble of interacting particles, employing a Gaussian ansatz for the joint distribution of the state and observation at each observation time. The EnKF is robust, but the Gaussian ansatz limits accuracy. We address this shortcoming by using machine learning to map the forecast distribution and observation to the filtering distribution. We propose cost functions that are minimised uniquely at the true filtering distribution. By time-averaging over trajectories in ergodic dynamical systems, the map can be learned and subsequently used for future filtering; this is a form of amortised Bayesian inference. We focus on learning ensemble-based filters within a mean field framework. We demonstrate the approach using a set transformer neural architecture, which is invariant to ensemble permutations. The learned filtering algorithms outperform state-of-the-art methods for filtering chaotic systems. They also perform well in challenging highly non-Gaussian and multimodal problems where the EnKF fails. Once learned at a given ensemble size, the learned map can be applied to other ensemble sizes with minimal fine-tuning.
30 Oct 2026	Sergey Dolgov (University of Bath)	TBC
30 Oct 2026	Michael Murray (University of Bath)	Generative AI discussion
6 Nov 2026	Federico Cornalba (University of Bath)	TBC
13 Nov 2026	NA+DS Group Members	Presenting project ideas to new SAMBa students
20 Nov 2026	Clara Hawkins (University of Bath)	TBC
20 Nov 2026	Bradley Earley (University of Bath)	TBC
27 Nov 2026	Luca Zanetti (University of Bath)	TBC
4 Dec 2026	MMath Students	Year-Long Projects
11 Dec 2026	Veronica Raffetto (University of Bath)	TBC
11 Dec 2026	Ben Dutton (University of Bath)	TBC

Subscribe to seminar calendar

You can subscribe to the NA calendar directly from your calendar client, including Outlook, Apple’s iCalendar or Google calendar. The web address of the calendar is this ICS link which you will need to copy.

To subscribe to a calendar in Outlook:

1. In Calendar view, select “Add Calendar” (large green +)
2. Select “From Internet”
3. Copy paste the ICS link, click OK, and click Yes to subscribe.

To subscribe to a calendar in iCalendar, please follow these instructions. Copy paste the ICS link in “web address”.

To subscribe to a calendar in Google Calendar:

1. Go to link.
2. On the left side go to "Other Calendars" and click on the dropdown.
3. Choose "Add by URL".
4. Copy paste the ICS link in the URL of the calendar.
5. Click on "Add Calendar" and wait for Google to import your events. This creates a calendar with a somewhat unreadable name.
6. To give a readable name to the calendar, click on the three vertical dots sign next to the newly created calendar and select Settings.
7. Choose a name for the calendar, eg. Numerical Analysis @ Bath, and click back button on top left.

How to get to Bath

See here for instructions how to get to Bath. Please email James Foster (jmf68@bath.ac.uk) and Michael Murray (mjm253@bath.ac.uk) if you intend to come by car and require a parking permit for Bath University Campus for the day.

Tips for giving talks

Tips for new students on giving talks

Since the audience of the NA seminar contains both PhD students and staff with quite wide interests and backgrounds, the following are some guidelines/hints to make sure people don't give you evil looks at lunch afterwards.

Before too much time passes in your talk, ideally the audience should know the answers to the following 4 questions:

• What is the problem you're considering?
• Why do you find this interesting?
• What has been done before on this problem/what's the background?
• What is your approach/what are you going to talk about?

There are lots of different ways to communicate this information. One way, if you're doing a slide show, could be for the first 4 slides to cover these 4 questions; although in this case you may want to revisit these points later on in the talk (e.g. to give more detail).

Remember:

• "vertebrate style" (structure hidden inside - like the skeleton of a vertebrate) = good for detective stories, bad for maths talks.
• "crustacean style" (structure visible from outside - like the skeleton of a crustacean) = bad for detective stories, good for maths talks.