Posters

In addition to the accepted papers, the following posters will be presented at the conference. The poster session will take place from 17:00 to 19:00 on Wednesday, 9 September.

• Nathanael Bosch (EPFL): Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs
  Abstract

  Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free update step that uses Jacobian-vector products, iterative linear solvers, and stochastic covariance estimation to enable linear scaling, all while retaining stability. Second, we propose iterative re-linearization to further improve stability without sacrificing scalability, turning probabilistic ODE solvers into fully implicit methods. We evaluate the proposed approaches on a range of stiff and high-dimensional problems and demonstrate improved stability and scalability over established probabilistic solvers.

• Jon Cockayne (University of Southampton): A Complete Theory of Affine Probabilistic Iterative Methods?
  Abstract

  Probabilistic linear solvers return distributions over the solution of \(Ax=b\), quantifying the uncertainty due to finite computation. The literature has long distinguished Bayesian solvers, which condition a prior on projections of the system, from probabilistic iterative methods (PIMs), which lift a classical iterative solver into probability space. We show this dichotomy is false: Bayesian solvers are a subclass of PIMs. We further prove that essentially every reasonable affine PIM is strongly calibrated, requiring only the benign fixed-point property in place of much stronger assumptions made in earlier work. Finally, we show that under the inverse prior, the posterior covariance automatically takes the downdate form required by applications such as computation-aware Gaussian processes.

• Olivier Dondjio (LUT University): Bayesian Optimization for Inhomogeneous Functions via Locally Adaptive Kernels
  Abstract

  Bayesian optimization (BO) is a popular global optimization technique that uses a Gaussian Process (GP) as a surrogate model for the objective function. Traditional BO methods often assume a stationary GP kernel, meaning that the function is assumed to have the same level of smoothness everywhere in the input space. However, many real-world objective functions exhibit varying smoothness across the input space. To address this limitation, we propose a BO framework that employs locally adaptive estimation of GP kernel hyperparameters, allowing the model to adapt to local variations in smoothness and improve optimization performance. Preliminary benchmark results show that our proposed framework successfully adapts to varying smoothness, consistently outperforming standard stationary baselines.

• Erik Englesson (University of Cambridge): A Chapman-Kolmogorov Perspective on Gradient-Based Optimization
  Abstract

  While optimizers drive the success of neural networks in domains such as protein folding and language modelling, their theoretical foundations remain unclear. Fundamental parts such as the learning rate, preconditioning matrix, and momentum are often viewed as heuristics rather than derived properties. This begs the question: Can gradient-based optimizers be derived from first principles? In this work, we aim to unify optimizers as different approximations of a single equation. We model the the trajectory of network parameters in space and time as a probability distribution evolving towards the modes of the posterior. This evolution is described by the Chapman-Kolmogorov equation, which yields an iterative algorithm that calculates marginal distributions: \(p(\theta_t)=\int p(\theta_t|\theta_{t-1})p(\theta_{t-1}) d\theta_{t-1}\) . To relate optimization algorithms with this iterative marginalization procedure, we need to specify: i) the initial distribution \(p(\theta_0)\), ii) the transition density \(p(\theta_t|\theta_{t-1})\) , and iii) a method to evaluate or approximate the marginalization integral. In the poster, we show how specific choices for the transition density, and marginal approximations recover different algorithms, including the Adam optimizer.

• Paul Fischer (University of Tübingen): Calibrating Latent Force ODE Filters
  Abstract

  Recovering the unknown input forces that drive dynamical systems, together with reliable uncertainty, is essential for downstream decisions in science and engineering. Hybrid approaches, such as latent force models, combine data-driven and mechanistic modelling. Latent force ordinary differential equation (ODE) filters achieve this by incorporating the mechanistic model as data during inference. The ODE residual enters the filter as a pseudo-observation, alongside real measurements. However, this flexibility also makes calibration challenging. We examine the calibration of latent force ODE filters and present a practical guide.

• Jarmo Flander (LUT University): A Weighted Regularization Model for Fourier Phase Retrieval with Gaussian White Noise
  Abstract

  We consider reconstructing a signal from its Fourier magnitude when an additional noisy prior is available. We formulate the reconstruction as the solution of a weighted regularization problem that balances the Fourier-magnitude information with a noisy prior corrupted by Gaussian white noise. The problem reduces to pointwise minimization in the Fourier domain, from which we derive an explicit formula for the minimizer. We also characterize the expectation of the resulting reconstruction in the sense of tempered distributions. Numerical examples demonstrate how the reconstruction changes with the noise level and illustrate the interaction between the magnitude data and the noisy prior.

• Alexandra Gessner (AstraZeneca): BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization
  Abstract

  Antibody lead optimization is inherently a multi-objective challenge in drug discovery. Achieving a balance between different drug-like properties is crucial for the development of viable candidates, and this search becomes exponentially challenging as desired properties grow. The ever-growing zoo of sophisticated in silico tools for predicting antibody properties calls for an efficient joint optimization procedure to overcome resource-intensive sequential filtering pipelines. We present BOAT, a versatile Bayesian optimization framework for multi-property antibody engineering. Our ‘plug-and-play’ framework couples uncertainty-aware surrogate modeling with a genetic algorithm to jointly optimize various predicted antibody traits while enabling efficient exploration of sequence space. Through systematic benchmarking against genetic algorithms and newer generative learning approaches, we demonstrate competitive performance with state-of-the-art methods for multi-objective protein optimization. We identify clear regimes where surrogate-driven optimization outperforms expensive generative approaches and establish practical limits imposed by sequence dimensionality and oracle costs.

• Philipp Guth (RICAM, Austrian Academy of Sciences): Dynamics Output-Feedback Stabilization of Uncertain Linear Dynamics via Digital Twins
  Abstract

  This work presents a digital twin framework for output-feedback stabilization and parameter identification in uncertain dynamical systems. A virtual model evolves in parallel with the physical process, assimilating measurement data in real time. By design, the digital twin reconstructs the system state and generates a stabilizing feedback, while model parameters are simultaneously inferred from data of the controlled dynamics using a Bayesian approach. Numerical results for the coupled physical-virtual dynamics demonstrate how digital twins can act jointly as observers, parameter estimators, and control agents, ensuring robust performance under uncertainty.

• Teemu Härkönen (Aalto University): Bayesian Estimation of Optical Constants Using Mixtures of Gaussian Process Experts
  Abstract

  We propose modeling absorption spectra using mixtures of Gaussian process experts. This provides a flexible statistical model for interpolating and extrapolating spectral measurements and for propagating the resulting uncertainty through the Kramers–Kronig relations to estimate the full complex refractive index. We additionally model the anchor points used in subtractive Kramers–Kronig relations probabilistically, accounting for uncertainty arising from measurement errors in the anchor values. The resulting formulation decouples the integral transform from the measurement grid, treating the unknown continuous spectrum rather than a fixed discretization as the object propagated through the Kramers–Kronig operator. This permits flexible numerical evaluation while retaining uncertainty associated with unresolved spectral information. Beyond flexible statistical modeling, the mixture-of-Gaussian-process-experts formulation enables automatic selection of measurement points informative for extrapolation. We demonstrate the method on experimental absorption spectra of gallium arsenide, potassium chloride, and transparent wood.

• Teemu Härkönen (Aalto University): Estimation of log-Gaussian Gamma Processes with Iterated Posterior Linearization and Hamiltonian Monte Carlo
  Abstract

  Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable, with the notable exception of Gaussian processes. Inference of models with non-Gaussian errors typically involves estimation of a high-dimensional latent variable. We propose two methods that use iterated posterior linearization followed by Hamiltonian Monte Carlo to sample the posterior distributions of such latent models with a particular focus on log-Gaussian gamma processes. In addition to more efficient estimation, iterated posterior linearization allows us to quantify the uncertainty of the linearization. The proposed methods are validated with two synthetic datasets generated from the log-Gaussian gamma process and a multiscale biocomposite stiffness model. In addition, we apply the methodology to an experimental Raman spectrum of argentopyrite.

• Disha Hegde (University of Southampton): Affine Tracing for Probabilistic Iterative Methods
  Abstract

  Affine probabilistic iterative methods (PIMs) have useful applications, especially with the inverse prior, but their practical adoption has been limited by the significant manual effort required to implement them. To address this, we introduce affine tracing, an algorithmic framework that automatically constructs a PIM from a standard implementation of an affine iterative method by passing symbolic tracers through the computation to build an affine computational graph. We show how this graph can be transformed to compute posterior covariances, as well as to perform algebraic simplifications required for computation under the inverse prior. We demonstrate this framework by automatically generating a probabilistic multigrid solver.

• Alex Ledbetter (TU Eindhoven): Inter-Domain Gaussian Processes with Arbitrary Mean Functions in Factor Graphs
  Abstract

  The modeling flexibility and expressivity of inter-domain Gaussian processes, enabled by applying arbitrary linear operators to a latent Gaussian process, is significant and desirable in robotics and probabilistic numerics communities. However, inter-domain Gaussian processes have not yet been available in a probabilistic message-passing formulation. In this paper, we formalize how to enable inter-domain observations for Gaussian processes in a variational message-passing framework. We develop a decoupled inter-domain variational sparse Gaussian process (dID-VSGP) model for univariate latent Gaussian processes with arbitrary mean functions, and derive the mean-field variational message-passing update rules that allow inference in this model. We validate our derivations in a shape exploration and modeling task, and by solution to a linear stochastic partial differential equation representative of physics-informed exploration. We confirm that our message-passing implementation maintains the same scaling complexity as the VSGP analytical solution. Our results further unify the analytical and message-passing approaches to variational inference and enable inter-domain observations in factor-graph Gaussian processes.

• Kai Lüdemann (University of Tübingen): Iteratively Expanding Diffusion Models with Gaussian Priors
  Abstract

  Diffusion models sample from complex, intractable distributions by iteratively reconstructing data samples from noise. They are a popular alternative to Gaussian process models for simulating high-dimensional processes. However, unlike Gaussian processes, increasing the dimension by adding grid points or pixels may require recomputing expensive inference passes or training a new model. In this work, we investigate approaches for iteratively expanding the dimension of diffusion models. Firstly, we propose a Gaussian diffusion model that admits iterative expansion by updating Cholesky decompositions. The lower triangular flow structure preserves trajectories in the original dimensions, enabling efficient inference by eliminating recomputation. Then, we implement this as a whitening step for sampling from posterior distributions with Gaussian priors and analytic likelihoods. Finally, we describe how the lower triangular map corresponds to a sequential conditioning structure within the denoising step. We aim to explore how linear encoders or causal masking may enable iterative expansion for neural diffusion models.

• Brandon O'Connell (University of Sheffield): Where to be Bayesian: A Subdomain View of Uncertainty in StatFEM for SHM
  Abstract

  Finite element (FE) methods underpin modern computational mechanics, but their predictive capability is fundamentally limited by modelling uncertainty arising from idealised assumptions, variability, and incomplete knowledge. Stochastic and statistical finite element methods, including the statistical FE method (statFEM), offer a principled route to quantifying this uncertainty, but their computational cost often renders them impractical for large-scale or complex systems. Engineering judgement, however, suggests that confidence in model fidelity is typically spatially localised — to specific materials, components, or subregions — whilst the rest of a domain can be considered well-characterised. In structural health monitoring (SHM), this localisation is characteristic of typical damage or degradation. We propose a subdomain-based approach that confines stochasticity to non-overlapping regions identified using such engineering insight, propagating the resulting uncertainty to the rest of the solution field via the Schur complement — which both condenses the global system onto the region of interest and yields an exact affine map for the exterior response. This substantially reduces the dimensionality of the stochastic problem while preserving a global estimate of uncertainty. Applied to static elasticity problems in structural mechanics, the approach achieves significant computational savings over conventional treatments without sacrificing prediction accuracy.

• Subhendu Pramanick (LUT University): Learning Smoothness of Matérn Gaussian Processes on Graphs
  Abstract

  This poster explores maximum likelihood estimation (MLE) for learning the smoothness parameter of Matérn Gaussian processes defined on graphs. By leveraging graph spectral properties and stochastic differential operator formulations, we analyze the consistency and sample complexity of recovering geometric regularity from discrete network observations.

• Herilalaina Rakotoarison (University of Helsinki): \(\alpha\)-PFN: Fast Entropy Search via In-Context Learning
  Abstract

  Information-theoretic acquisition functions such as Entropy Search (ES) offer a principled exploration–exploitation framework for Bayesian optimization (BO). However, their practical implementation relies on complicated and slow approximations, i.e., a Monte Carlo estimation of the information gain. This complexity can introduce numerical errors and requires specialized, hand-crafted implementations. We propose a two-stage amortization strategy that learns to approximate entropy search-based acquisition functions using Prior-data Fitted Networks (PFNs) in a single forward pass. A first PFN is trained to be conditioned on information about the optima; second, the \(\alpha\)-PFN is trained to predict the expected information gain by training on information gains measured with the first PFN. The \(\alpha\)-PFN offers a flexible learned approximation, which replaces the complex heuristic approximations with a single forward pass per candidate, enabling rapid and extensible acquisition evaluation. Empirically, our approach is competitive with state-of-the-art entropy search implementations on synthetic and real-world benchmarks, while accelerating the different entropy search variants across all our experiments, with speed ups over 50x.

• Abdullah Tokmak (Aalto University and Nokia Bell Labs): Safe Learning-Based Control via Function-Based Uncertainty Quantification
  Abstract

  Uncertainty quantification is essential when deploying learning-based control methods in safety-critical systems. This is commonly realized by constructing uncertainty tubes that enclose the unknown function of interest—e.g., the reward and constraint functions, or the underlying dynamics model—with high probability. However, existing approaches for uncertainty quantification typically rely on restrictive assumptions on the unknown function, such as a known norm in a function space, and struggle with discontinuities. In this paper, we model the unknown function as a random function from which independent and identically distributed realizations can be generated, and construct uncertainty tubes via the scenario approach that hold with high probability and rely solely on the sampled realizations. We integrate these uncertainty tubes into a safe Bayesian optimization algorithm, which we then use to safely tune control parameters on a real Furuta pendulum.

• Eliott Van Dieren (EPFL): Functional Bayesian Optimization for PDE-Constrained Problems
  Abstract

  PDE-constrained optimization problems arise in many scientific and engineering applications, where objective evaluations require solving a partial differential equation. These problems are often expensive and may involve optimization over function spaces, for example when controls or designs are spatially distributed. Bayesian optimization provides a data-efficient framework for expensive black-box optimization, but is usually formulated for finite-dimensional parameter spaces. If applied naively to discretized functional inputs, its performance may deteriorate as the input dimension grows. In this work, we study Bayesian optimization over functional inputs for PDE-constrained problems. We use functional Gaussian process priors with covariance kernels defined through Sobolev or operator-induced norms, allowing the surrogate model to incorporate structural information from the underlying PDE system. We investigate how these kernel choices affect surrogate modeling, acquisition optimization, and the exploration of candidate controls. Numerical experiments on linear and nonlinear elliptic PDE-constrained control problems demonstrate the practical impact of operator-informed kernels and their mesh-robust behavior under refinement.

• Niall Vyas (University of Southampton): Generalised Bayesian Probabilistic Numerical Methods
  Abstract

  Bayesian PNMs typically condition on noise-free data, meaning that the posterior is often singular with respect to the prior. This makes standard KL-based variational inference ill-posed. We introduce GenBPNM, a generalised Bayesian objective that replaces the KL divergence with a 2-Wasserstein distance, which remains finite under mismatched supports. In the linear-Gaussian setting the minimiser recovers the posterior mean exactly while returning a more concentrated covariance. Empirically, GenBPNM improves the calibration of BayesCG, and we assess its accuracy and calibration across a range of nonlinear differential equation problems solved using stochastic variational Gaussian processes.

• Kyrylo Yemets (Lviv Polytechnic National University): Composing Non-Conjugate Factor Graphs
  Abstract

  Stacking probabilistic building blocks into deeper architectures typically breaks closed-form inference. We show that closed-form inference can be preserved. We identify five factor-graph primitives: a bilinear factor, an exponential link, a Gamma prior, a Gaussian likelihood, and an equality node, and prove that any model composed from them admits closed-form variational message passing. The construction works because each primitive preserves a small set of message families: under mean-field factorization, messages on Gaussian variables remain Gaussian and messages on precision variables remain Gamma, while the only non-conjugate interface, the exponential link, remains tractable through the Gaussian moment-generating function and the sufficient statistics of the Gamma family. We demonstrate composition at increasing depth, from static ensembles through input-dependent gating to split-branch routing, and show that stacking routing layers encodes arbitrary decision trees, establishing universal function approximation with closed-form inference. Applied to ensemble time-series forecasting, the framework yields a Bayesian mixture of experts in which gating functions are inferred rather than learned, providing calibrated uncertainty over expert selection across five benchmark datasets.