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Cornelius Schröder

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6 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

FNOPE: Simulation-based inference on function spaces with Fourier Neural Operators

Guy Moss
Leah Muhle
Reinhard Drews
Jakob H Macke
Cornelius Schröder

Simulation-based inference (SBI) is an established approach for performing Bayesian inference on scientific simulators. SBI so far works best on low-dimensional parametric models. However, it is difficult to infer function-valued parameters, which frequently occur in disciplines that model spatiotemporal processes such as the climate and earth sciences. Here, we introduce an approach for efficient posterior estimation, using a Fourier Neural Operator (FNO) architecture with a flow matching objective. We show that our approach, FNOPE, can perform inference of function-valued parameters at a fraction of the simulation budget of state of the art methods. In addition, FNOPE supports posterior evaluation at arbitrary discretizations of the domain, as well as simultaneous estimation of vector-valued parameters. We demonstrate the effectiveness of our approach on several benchmark tasks and a challenging spatial inference task from glaciology. FNOPE extends the applicability of SBI methods to new scientific domains by enabling the inference of function-valued parameters.

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TMLR Journal 2024 Journal Article

A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science

Sebastian Bischoff
Alana Darcher
Michael Deistler
Richard Gao
Franziska Gerken
Manuel Gloeckler
Lisa Haxel
Jaivardhan Kapoor

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the samples these models generate? This work aims to provide an accessible entry point to understanding popular sample-based statistical distances, requiring only foundational knowledge in mathematics and statistics. We focus on four commonly used notions of statistical distances representing different methodologies: Using low-dimensional projections (Sliced-Wasserstein; SW), obtaining a distance using classifiers (Classifier Two-Sample Tests; C2ST), using embeddings through kernels (Maximum Mean Discrepancy; MMD), or neural networks (Fréchet Inception Distance; FID). We highlight the intuition behind each distance and explain their merits, scalability, complexity, and pitfalls. To demonstrate how these distances are used in practice, we evaluate generative models from different scientific domains, namely a model of decision-making and a model generating medical images. We showcase that distinct distances can give different results on similar data. Through this guide, we aim to help researchers to use, interpret, and evaluate statistical distances for generative models in science.

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ICML Conference 2024 Conference Paper

Simultaneous identification of models and parameters of scientific simulators

Cornelius Schröder
Jakob H. Macke

Many scientific models are composed of multiple discrete components, and scientists often make heuristic decisions about which components to include. Bayesian inference provides a mathematical framework for systematically selecting model components, but defining prior distributions over model components and developing associated inference schemes has been challenging. We approach this problem in a simulation-based inference framework: We define model priors over candidate components and, from model simulations, train neural networks to infer joint probability distributions over both model components and associated parameters. Our method, simulation-based model inference (SBMI), represents distributions over model components as a conditional mixture of multivariate binary distributions in the Grassmann formalism. SBMI can be applied to any compositional stochastic simulator without requiring likelihood evaluations. We evaluate SBMI on a simple time series model and on two scientific models from neuroscience, and show that it can discover multiple data-consistent model configurations, and that it reveals non-identifiable model components and parameters. SBMI provides a powerful tool for data-driven scientific inquiry which will allow scientists to identify essential model components and make uncertainty-informed modelling decisions.

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NeurIPS Conference 2024 Conference Paper

Sourcerer: Sample-based Maximum Entropy Source Distribution Estimation

Julius Vetter
Guy Moss
Cornelius Schröder
Richard Gao
Jakob H. Macke

Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since many different source distributions might produce the same distribution of data-consistent simulations. To make a principled choice among many equally valid sources, we propose an approach which targets the maximum entropy distribution, i. e. , prioritizes retaining as much uncertainty as possible. Our method is purely sample-based - leveraging the Sliced-Wasserstein distance to measure the discrepancy between the dataset and simulations - and thus suitable for simulators with intractable likelihoods. We benchmark our method on several tasks, and show that it can recover source distributions with substantially higher entropy than recent source estimation methods, without sacrificing the fidelity of the simulations. Finally, to demonstrate the utility of our approach, we infer source distributions for parameters of the Hodgkin-Huxley model from experimental datasets with hundreds of single-neuron measurements. In summary, we propose a principled method for inferring source distributions of scientific simulator parameters while retaining as much uncertainty as possible.

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NeurIPS Conference 2020 Conference Paper

System Identification with Biophysical Constraints: A Circuit Model of the Inner Retina

Cornelius Schröder
David Klindt
Sarah Strauss
Katrin Franke
Matthias Bethge
Thomas Euler
Philipp Berens

Visual processing in the retina has been studied in great detail at all levels such that a comprehensive picture of the retina's cell types and the many neural circuits they form is emerging. However, the currently best performing models of retinal function are black-box CNN models which are agnostic to such biological knowledge. In particular, these models typically neglect the role of the many inhibitory circuits involving amacrine cells and the biophysical mechanisms underlying synaptic release. Here, we present a computational model of temporal processing in the inner retina, including inhibitory feedback circuits and realistic synaptic release mechanisms. Fit to the responses of bipolar cells, the model generalized well to new stimuli including natural movie sequences, performing on par with or better than a benchmark black-box model. In pharmacology experiments, the model replicated in silico the effect of blocking specific amacrine cell populations with high fidelity, indicating that it had learned key circuit functions. Also, more in depth comparisons showed that connectivity patterns learned by the model were well matched to connectivity patterns extracted from connectomics data. Thus, our model provides a biologically interpretable data-driven account of temporal processing in the inner retina, filling the gap between purely black-box and detailed biophysical modeling.

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NeurIPS Conference 2019 Conference Paper

Approximate Bayesian Inference for a Mechanistic Model of Vesicle Release at a Ribbon Synapse

Cornelius Schröder
Ben James
Leon Lagnado
Philipp Berens

The inherent noise of neural systems makes it difficult to construct models which accurately capture experimental measurements of their activity. While much research has been done on how to efficiently model neural activity with descriptive models such as linear-nonlinear-models (LN), Bayesian inference for mechanistic models has received considerably less attention. One reason for this is that these models typically lead to intractable likelihoods and thus make parameter inference difficult. Here, we develop an approximate Bayesian inference scheme for a fully stochastic, biophysically inspired model of glutamate release at the ribbon synapse, a highly specialized synapse found in different sensory systems. The model translates known structural features of the ribbon synapse into a set of stochastically coupled equations. We approximate the posterior distributions by updating a parametric prior distribution via Bayesian updating rules and show that model parameters can be efficiently estimated for synthetic and experimental data from in vivo two-photon experiments in the zebrafish retina. Also, we find that the model captures complex properties of the synaptic release such as the temporal precision and outperforms a standard GLM. Our framework provides a viable path forward for linking mechanistic models of neural activity to measured data.

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