2026 Abstracts

Title: Bridging domain decomposition and scientific machine learning for PDEs

Abstract:
Solving large-scale PDEs at the frontier of modern applications increasingly requires combining the rigour and scalability of classical numerical methods with the flexibility of machine learning. In this talk I will discuss how ideas from domain decomposition - locality, coarse-space correction, and parallel scalability - can inform and improve neural network–based approaches to PDEs, and conversely how SciML techniques can enrich classical solvers. I will illustrate these connections through a few representative problems, ranging from wave propagation to multiscale models, and outline open questions and opportunities for the broader community working on numerical approximation of PDEs.

Title: Data assimialtion: from climite science to neuroscience

Abstract:
Data assimilation is concerned with estimating the initial state of a chaotic dynamical system from available measurement data. Over the years, this classical definition has been broadened to encompass parameter estimation and model error estimation. Furthermore, while data assimilation was initially applied primarily in fluid dynamics — for example in weather forecasting — it is now used across many other domains, such as neuroscience.

In this talk, I will introduce the Bayesian data assimilation framework, in which the goal is not a single estimate but an ensemble of estimates that reconstruct the posterior distribution given the prior and the data. The challenge is twofold: one must have theoretical guarantees that the inverse problem is well-posed, and one must sample the posterior in a computationally efficient manner. I will present theoretical results for the inverse problem of a model describing neuronal activity in the brain, as well as computational results for a high-dimensional PDE-constrained inverse problem.

Title: Scalable Wave Solvers in Large-Scale Scientific Computing: From Convergence to Energy Efficiency

Abstract:
Wave simulations are central to many areas of scientific computing, but their large-scale numerical solution remains challenging. Increasing model fidelity and grid resolution lead to stiff,strongly coupled, and often severely ill-conditioned systems, for which standard solvers may stagnate. These bottlenecks increasingly affect not only runtime and iteration count, but also energy-to-solution on modern architectures. At the same time, AI-based solvers are reshaping the field by offering new routes to acceleration. However, these methods also introduce their own costs and unresolved questions of robustness. This talk examines scalable wave solvers through the combined lens of convergence, accuracy, and energy efficiency. We focus on multilevel methods and advanced preconditioning strategies as mechanisms for improving convergence, and as paradigms in providing both practical tools for deployment and useful benchmarks for emerging approaches. The talk concludes by asserting that future solver development should move beyond standard metrics and should adopt a systems approach that connects algorithmic design to hardware execution and energy use.

Title: Structure-preserving model reduction: From the formulation on manifolds to data-driven realizations

Title: Dealing with singularities in numerical methods

Title:   Multiharmonic Algorithms for Contrast-Enhanced Ultrasound

Abstract:  
Nonlinear acoustic effects physically underpin various medical and industrial applications of ultrasound.  Harmonic generation, in particular, plays a key role in contrast-enhanced ultrasound, for both imaging and therapeutic applications. We will discuss models for the interaction of ultrasound waves with contrast agents, in which the acoustic field is governed by a nonlinear Westervelt-type wave equation coupled to a Rayleigh-Plesset-type ODE that describes the dynamics of microbubble contrast agents. This coupling gives rise to nontrivial analytical and computational questions, including the existence of time-periodic solutions and the handling of nonlinearity and differing time scales. Direct time-domain simulation is prohibitively expensive for capturing nonlinear effects, which motivates a frequency-domain discretization based on a multiharmonic Ansatz applied to the wave–bubble system.  We will present a priori error estimates that characterize the approximation error in terms of the number of retained harmonics and a contribution arising from the fixed-point iteration. Additionally, numerical experiments will illustrate how the number of retained harmonics and the presence of microbubbles influence ultrasound propagation. The talk is based on joint work with Teresa Rauscher (University of Graz, Austria).

Title: RIDGE: An Autonomous Framework for Validation and Method Discovery in AI-Generated Option Pricing

Abstract:
Automated code generation is finding increasing application in quantitative finance, where large language models can generate option pricing implementations directly from mathematical model specifications. Validating such implementations, however, requires more than standard unit tests: numerical pricing methods must remain mathematically consistent, numerically stable, and robust across a wide range of model parameters.
We present RIDGE, an autonomous validation methodology in which generated pricing implementations are subjected to structured no-arbitrage checks, stress tests, benchmark comparisons, and consistency inspections. Diagnostic knowledge accumulated during the validation process is stored and reused across models and validation cycles, enabling systematic improvement of both the pricing implementation and the validation methodology itself.
Applied to five stochastic volatility models, the methodology eliminates all detected implementation defects and, in two cases, leads to new semi-analytic pricing constructions.
Focus will however be on numerical mathematics aspects.
By Kees Oosterlee,
Joint work with: Liexin Cheng (Peking University),  Shuaiqiang Liu (TU Delft)

Title: Adaptive methods for nonlinear, doubly-degenerate diffusion equations

Abstract:
Degenerate parabolic equations appear as mathematical models for many situations of practical relevance. Among these we mention porous media flows, or reactive transport, biofilms, but also phase change or tumour growth. In such equations, the nonlinear diffusion coefficient may vanish or blow up for certain values of the unknown, leading to a change in the character of the equation from parabolic into hyperbolic, or elliptic. The regions in which the equation has one or another type are not known a priori, and are separated by so-called free boundaries. Usually, the solution lacks regularity, which makes the mathematical and numerical analysis for such equations a challenging task.
Motivated by the low regularity of the solution, we consider an Euler implicit time-stepping, leading to a sequence of nonlinear, time-discrete problems. These are reformulated in terms of a new unknown, which allows working with nonlinearities that are Lipschitz continuous, though maybe not strictly monotone. For the resulting equations, a splitting strategy is applied, which leads to a formulation that is more suitable for dealing with the degeneracies. Based on this splitting, different iterative linearisation strategies are considered.
After presenting some convergence results, we focus on a scheme that combines ideas related to Banach contraction arguments and to the Newton scheme (the so-called M-scheme). This scheme converges under mild restrictions for the time step, but for any spatial discretisation and mesh. We further present an adaptive strategy for selecting the optimal parameters, relying on a posteriori estimations. This strategy accelerates the convergence of the M-scheme while preserving its robust convergence w.r.t. to the spatial discretisation. Moreover, the adaptive M-scheme consistently out-competes the Newton scheme, showing quadratic convergence behavior.
Finally, if time allows we discuss an iterative scheme using the same splitting strategy, but designed at the level of the fully continuous problem. For this, an adaptive space-time discretisation is presented.
This work is done jointly with Ayesha Javed (Hasselt) and Koondanibha Mitra (Eindhoven) 

tba

Title: Monolitic solvers for parabolic PDEs

Abstract:
The classical approach to solving parabolic partial differential equations (PDEs) relies on time-marching schemes. This talk discusses alternative solution techniques based on a simultaneous space-time variational formulation. Key advantages of this framework include guaranteed quasi-best approximations (Céa's lemma), enhanced parallel complexity, and adaptive refinements localized in both space and time.

Title: Efficient numerical solution of PIDEs for electricity derivatives under jump dynamics

Abstract:
This talk presents recent advances in the numerical solution of partial integro-differential equations (PIDEs) arising in electricity derivatives pricing under jump dynamics.
First, we consider swing options, widely traded in electricity markets. These contracts grant the holder the right to purchase electricity dynamically at a fixed price, subject to operational constraints, thereby mitigating exposure to strong price fluctuations. The spot price is modeled by a two-factor mean-reverting jump-diffusion process with finite activity, leading—via dynamic programming—to a sequence of parabolic PIDEs.
Second, we address the valuation of options, where the payoff depends on the price of multiple energy commodities. Here, the underlying dynamics are driven by infinite-activity jumps, resulting in PIDEs with singular integral terms.
To solve these problems, we develop efficient finite difference schemes with particular attention to the accurate and stable treatment of the nonlocal integral operators. The proposed methods are supported by a rigorous convergence analysis and demonstrate strong performance in multidimensional settings.

based on joint work with Mustapha Regragui (UGent), Massimiliano Moda (UAntwerp), Karel in 't Hout (UAntwerp) and Fred Espen Benth (BI Norwegian Business School)

Title: Inequality constraints and Krylov subspace methods. 

Abstract:
Krylov methods such as conjugate gradients, BiCGstab, and LSQR are an essential building block for solving large-scale problems in computational science. They can handle sparse systems of equations with billions of variables and scale to the largest supercomputers.

Many industrial problems, however, involve inequality constraints. These arise, for example, when modelling contact between mechanical parts, or as non-negativity constraints that capture physical quantities such as density or encode prior knowledge in data science.

We discuss how these subspace methods can be generalised to incorporate such inequality constraints, and illustrate the approach on several industrially relevant problems.

Title: Large Eddy Simulation of  Turbulence Through Integrated Filtering, Modeling and Discretization

Abstract:
Large Eddy Simulation (LES) resolves turbulent motions above a filter scale and models those below it. Filtering, modeling, and discretization are treated as a single, integrated framework. Using finite volumes introduces two spatial filters: one from averaging over grid cells and another from interpolating values to cell faces for flux evaluation. The interpolation filter sets the effective flux resolution and thus determines which eddies are actually resolved. Small‑scale effects are modeled to keep total variation bounded, ensuring that the numerical scheme behaves consistently with the physical intend of filtering and does not introduce spurious small scale motions.

Title: The Art of Geometric Paper Folding

Abstract:
After 22 years of employment as a professor in numerical analysis, first with the TUD and then with the UU, I am since my retirement in 2006 full time involved in graphical design and paper folding.
With paper folding, I am mainly interested in the design of 3-D paper sculptures and the combination with (my) graphical designs. The basic folding techniques used, are more widely known as geometric and modular folding. In my presentation I will give an overview and I will touch mathematical aspects.