Christoph Weniger

Benjamin Kurt Miller, Christoph Weniger, Patrick Forré

Likelihood-to-evidence ratio estimation is usually cast as either a binary (NRE-A) or a multiclass (NRE-B) classification task. In contrast to the binary classification framework, the current formulation of the multiclass version has an intrinsic and unknown bias term, making otherwise informative diagnostics unreliable. We propose a multiclass framework free from the bias inherent to NRE-B at optimum, leaving us in the position to run diagnostics that practitioners depend on. It also recovers NRE-A in one corner case and NRE-B in the limiting case. For fair comparison, we benchmark the behavior of all algorithms in both familiar and novel training regimes: when jointly drawn data is unlimited, when data is fixed but prior draws are unlimited, and in the commonplace fixed data and parameters setting. Our investigations reveal that the highest performing models are distant from the competitors (NRE-A, NRE-B) in hyperparameter space. We make a recommendation for hyperparameters distinct from the previous models. We suggest two bounds on the mutual information as performance metrics for simulation-based inference methods, without the need for posterior samples, and provide experimental results. This version corrects a minor implementation error in $γ$, improving results.

Arnaud Delaunoy, Benjamin Kurt Miller, Patrick Forré et al.

Conservative inference is a major concern in simulation-based inference. It has been shown that commonly used algorithms can produce overconfident posterior approximations. Balancing has empirically proven to be an effective way to mitigate this issue. However, its application remains limited to neural ratio estimation. In this work, we extend balancing to any algorithm that provides a posterior density. In particular, we introduce a balanced version of both neural posterior estimation and contrastive neural ratio estimation. We show empirically that the balanced versions tend to produce conservative posterior approximations on a wide variety of benchmarks. In addition, we provide an alternative interpretation of the balancing condition in terms of the $χ^2$ divergence.

Benjamin Kurt Miller, Marco Federici, Christoph Weniger et al.

In Simulation-based Inference, the goal is to solve the inverse problem when the likelihood is only known implicitly. Neural Posterior Estimation commonly fits a normalized density estimator as a surrogate model for the posterior. This formulation cannot easily fit unnormalized surrogates because it optimizes the Kullback-Leibler divergence. We propose to optimize a generalized Kullback-Leibler divergence that accounts for the normalization constant in unnormalized distributions. The objective recovers Neural Posterior Estimation when the model class is normalized and unifies it with Neural Ratio Estimation, combining both into a single objective. We investigate a hybrid model that offers the best of both worlds by learning a normalized base distribution and a learned ratio. We also present benchmark results.

Florian List, Noemi Anau Montel, Christoph Weniger

Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to observations are readily available for many applications. We present a versatile Bayesian field reconstruction algorithm rooted in simulation-based inference and enhanced by autoregressive modeling. The proposed technique is applicable to generic (non-differentiable) forward simulators and allows sampling from the posterior for the underlying field. We show first promising results on a proof-of-concept application: the recovery of cosmological initial conditions from late-time density fields.

Alex Cole, Benjamin Kurt Miller, Samuel J. Witte et al.

Sampling-based inference techniques are central to modern cosmological data analysis; these methods, however, scale poorly with dimensionality and typically require approximate or intractable likelihoods. In this paper we describe how Truncated Marginal Neural Ratio Estimation (TMNRE) (a new approach in so-called simulation-based inference) naturally evades these issues, improving the $(i)$ efficiency, $(ii)$ scalability, and $(iii)$ trustworthiness of the inferred posteriors. Using measurements of the Cosmic Microwave Background (CMB), we show that TMNRE can achieve converged posteriors using orders of magnitude fewer simulator calls than conventional Markov Chain Monte Carlo (MCMC) methods. Remarkably, the required number of samples is effectively independent of the number of nuisance parameters. In addition, a property called \emph{local amortization} allows the performance of rigorous statistical consistency checks that are not accessible to sampling-based methods. TMNRE promises to become a powerful tool for cosmological data analysis, particularly in the context of extended cosmologies, where the timescale required for conventional sampling-based inference methods to converge can greatly exceed that of simple cosmological models such as $Λ$CDM. To perform these computations, we use an implementation of TMNRE via the open-source code \texttt{swyft}.

Benjamin Kurt Miller, Alex Cole, Gilles Louppe et al.

We present algorithms (a) for nested neural likelihood-to-evidence ratio estimation, and (b) for simulation reuse via an inhomogeneous Poisson point process cache of parameters and corresponding simulations. Together, these algorithms enable automatic and extremely simulator efficient estimation of marginal and joint posteriors. The algorithms are applicable to a wide range of physics and astronomy problems and typically offer an order of magnitude better simulator efficiency than traditional likelihood-based sampling methods. Our approach is an example of likelihood-free inference, thus it is also applicable to simulators which do not offer a tractable likelihood function. Simulator runs are never rejected and can be automatically reused in future analysis. As functional prototype implementation we provide the open-source software package swyft.

Kristian G. Barman, Sascha Caron, Emily Sullivan et al.

This paper explores ideas and provides a potential roadmap for the development and evaluation of physics-specific large-scale AI models, which we call Large Physics Models (LPMs). These models, based on foundation models such as Large Language Models (LLMs) - trained on broad data - are tailored to address the demands of physics research. LPMs can function independently or as part of an integrated framework. This framework can incorporate specialized tools, including symbolic reasoning modules for mathematical manipulations, frameworks to analyse specific experimental and simulated data, and mechanisms for synthesizing theories and scientific literature. We begin by examining whether the physics community should actively develop and refine dedicated models, rather than relying solely on commercial LLMs. We then outline how LPMs can be realized through interdisciplinary collaboration among experts in physics, computer science, and philosophy of science. To integrate these models effectively, we identify three key pillars: Development, Evaluation, and Philosophical Reflection. Development focuses on constructing models capable of processing physics texts, mathematical formulations, and diverse physical data. Evaluation assesses accuracy and reliability by testing and benchmarking. Finally, Philosophical Reflection encompasses the analysis of broader implications of LLMs in physics, including their potential to generate new scientific understanding and what novel collaboration dynamics might arise in research. Inspired by the organizational structure of experimental collaborations in particle physics, we propose a similarly interdisciplinary and collaborative approach to building and refining Large Physics Models. This roadmap provides specific objectives, defines pathways to achieve them, and identifies challenges that must be addressed to realise physics-specific large scale AI models.

Oleg Savchenko, Guillermo Franco Abellán, Florian List et al.

Knowledge of the primordial matter density field from which the large-scale structure of the Universe emerged over cosmic time is of fundamental importance for cosmology. However, reconstructing these cosmological initial conditions from late-time observations is a notoriously difficult task, which requires advanced cosmological simulators and sophisticated statistical methods to explore a multi-million-dimensional parameter space. We show how simulation-based inference (SBI) can be used to tackle this problem and to obtain data-constrained realisations of the primordial dark matter density field in a simulation-efficient way with general non-differentiable simulators. Our method is applicable to full high-resolution dark matter $N$-body simulations and is based on modelling the posterior distribution of the constrained initial conditions to be Gaussian with a diagonal covariance matrix in Fourier space. As a result, we can generate thousands of posterior samples within seconds on a single GPU, orders of magnitude faster than existing methods, paving the way for sequential SBI for cosmological fields. Furthermore, we perform an analytical fit of the estimated dependence of the covariance on the wavenumber, effectively transforming any point-estimator of initial conditions into a fast sampler. We test the validity of our obtained samples by comparing them to the true values with summary statistics and performing a Bayesian consistency test.

Noemi Anau Montel, James Alvey, Christoph Weniger

Model misspecification analysis strategies, such as anomaly detection, model validation, and model comparison are a key component of scientific model development. Over the last few years, there has been a rapid rise in the use of simulation-based inference (SBI) techniques for Bayesian parameter estimation, applied to increasingly complex forward models. To move towards fully simulation-based analysis pipelines, however, there is an urgent need for a comprehensive simulation-based framework for model misspecification analysis. In this work, we provide a solid and flexible foundation for a wide range of model discrepancy analysis tasks, using distortion-driven model misspecification tests. From a theoretical perspective, we introduce the statistical framework built around performing many hypothesis tests for distortions of the simulation model. We also make explicit analytic connections to classical techniques: anomaly detection, model validation, and goodness-of-fit residual analysis. Furthermore, we introduce an efficient self-calibrating training algorithm that is useful for practitioners. We demonstrate the performance of the framework in multiple scenarios, making the connection to classical results where they are valid. Finally, we show how to conduct such a distortion-driven model misspecification test for real gravitational wave data, specifically on the event GW150914.

Oleg Savchenko, Florian List, Guillermo Franco Abellán et al.

Reconstructing cosmological initial conditions (ICs) from late-time observations is a difficult task, which relies on the use of computationally expensive simulators alongside sophisticated statistical methods to navigate multi-million dimensional parameter spaces. We present a simple method for Bayesian field reconstruction based on modeling the posterior distribution of the initial matter density field to be diagonal Gaussian in Fourier space, with its covariance and the mean estimator being the trainable parts of the algorithm. Training and sampling are extremely fast (training: $\sim 1 \, \mathrm{h}$ on a GPU, sampling: $\lesssim 3 \, \mathrm{s}$ for 1000 samples at resolution $128^3$), and our method supports industry-standard (non-differentiable) $N$-body simulators. We verify the fidelity of the obtained IC samples in terms of summary statistics.

Huifang Lyu, James Alvey, Noemi Anau Montel et al.

Simulation-based inference (SBI) is emerging as a new statistical paradigm for addressing complex scientific inference problems. By leveraging the representational power of deep neural networks, SBI can extract the most informative simulation features for the parameters of interest. Sequential SBI methods extend this approach by iteratively steering the simulation process towards the most relevant regions of parameter space. This is typically implemented through an algorithmic structure, in which simulation and network training alternate over multiple rounds. This strategy is particularly well suited for high-precision inference in high-dimensional settings, which are commonplace in physics applications with growing data volumes and increasing model fidelity. Here, we introduce dynamic SBI, which implements the core ideas of sequential methods in a round-free, asynchronous, and highly parallelisable manner. At its core is an adaptive dataset that is iteratively transformed during inference to resemble the target observation. Simulation and training proceed in parallel: trained networks are used both to filter out simulations incompatible with the data and to propose new, more promising ones. Compared to round-based sequential methods, this asynchronous structure can significantly reduce simulation costs and training overhead. We demonstrate that dynamic SBI achieves significant improvements in simulation and training efficiency while maintaining inference performance. We further validate our framework on two challenging astrophysical inference tasks: characterising the stochastic gravitational wave background and analysing strong gravitational lensing systems. Overall, this work presents a flexible and efficient new paradigm for sequential SBI.

Sascha Caron, Andreas Ipp, Gert Aarts et al.

Artificial intelligence (AI) is transforming scientific research, with deep learning methods playing a central role in data analysis, simulations, and signal detection across particle, nuclear, and astroparticle physics. Within the JENA communities-ECFA, NuPECC, and APPEC-and as part of the EuCAIF initiative, AI integration is advancing steadily. However, broader adoption remains constrained by challenges such as limited computational resources, a lack of expertise, and difficulties in transitioning from research and development (R&D) to production. This white paper provides a strategic roadmap, informed by a community survey, to address these barriers. It outlines critical infrastructure requirements, prioritizes training initiatives, and proposes funding strategies to scale AI capabilities across fundamental physics over the next five years.

Benjamin Kurt Miller, Alex Cole, Patrick Forré et al.

Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural simulation-based inference algorithm which simultaneously offers simulation efficiency and fast empirical posterior testability, which is unique among modern algorithms. Our approach is simulation efficient by simultaneously estimating low-dimensional marginal posteriors instead of the joint posterior and by proposing simulations targeted to an observation of interest via a prior suitably truncated by an indicator function. Furthermore, by estimating a locally amortized posterior our algorithm enables efficient empirical tests of the robustness of the inference results. Since scientists cannot access the ground truth, these tests are necessary for trusting inference in real-world applications. We perform experiments on a marginalized version of the simulation-based inference benchmark and two complex and narrow posteriors, highlighting the simulator efficiency of our algorithm as well as the quality of the estimated marginal posteriors.

Joeri Hermans, Nilanjan Banik, Christoph Weniger et al.

A statistical analysis of the observed perturbations in the density of stellar streams can in principle set stringent contraints on the mass function of dark matter subhaloes, which in turn can be used to constrain the mass of the dark matter particle. However, the likelihood of a stellar density with respect to the stream and subhaloes parameters involves solving an intractable inverse problem which rests on the integration of all possible forward realisations implicitly defined by the simulation model. In order to infer the subhalo abundance, previous analyses have relied on Approximate Bayesian Computation (ABC) together with domain-motivated but handcrafted summary statistics. Here, we introduce a likelihood-free Bayesian inference pipeline based on Amortised Approximate Likelihood Ratios (AALR), which automatically learns a mapping between the data and the simulator parameters and obviates the need to handcraft a possibly insufficient summary statistic. We apply the method to the simplified case where stellar streams are only perturbed by dark matter subhaloes, thus neglecting baryonic substructures, and describe several diagnostics that demonstrate the effectiveness of the new method and the statistical quality of the learned estimator.

Arnaud Delaunoy, Antoine Wehenkel, Tanja Hinderer et al.

Gravitational waves from compact binaries measured by the LIGO and Virgo detectors are routinely analyzed using Markov Chain Monte Carlo sampling algorithms. Because the evaluation of the likelihood function requires evaluating millions of waveform models that link between signal shapes and the source parameters, running Markov chains until convergence is typically expensive and requires days of computation. In this extended abstract, we provide a proof of concept that demonstrates how the latest advances in neural simulation-based inference can speed up the inference time by up to three orders of magnitude -- from days to minutes -- without impairing the performance. Our approach is based on a convolutional neural network modeling the likelihood-to-evidence ratio and entirely amortizes the computation of the posterior. We find that our model correctly estimates credible intervals for the parameters of simulated gravitational waves.