Dynamic SBI: Round-free Sequential Simulation-Based Inference with Adaptive Datasets

TL;DR

Dynamic SBI addresses the computational bottlenecks of simulation-based inference by making simulation and training asynchronous and by continuously updating a live dataset $\mathcal{D}_{\mathrm{live}}$ and a tempered proposal $\tilde{p}(\mathbf z)$ to target the observed data $\mathbf x_{obs}$. It introduces two methods, DS-A and DS-B, that prune uninformative samples and adapt proposals to concentrate simulations where information is gained, while ensuring recovery of the true posterior $p(\mathbf z\mid \mathbf x)$ through appropriate corrections or weighting. The framework is validated on a 10D synthetic benchmark and two astrophysical problems—the stochastic gravitational wave background and strong gravitational lensing—demonstrating accurate posterior recovery with substantially fewer simulations than amortised or round-based approaches and indicating strong potential for scaling to large, complex models like LISA data. The work also situates dynamic SBI within the continuum limit of sequential SBI and outlines future extensions to hierarchical, multi-fidelity, and distributed inference, highlighting its practical impact for high-cost scientific analyses.

Abstract

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.

Figures (8)

• Figure 1: Dynamic simulation-based inference: Summary figure detailing the dynamic SBI framework. The framework splits into two core process types: a) a simulation process which updates (via deletion/re-simulation) a live dataset $\mathcal{D}_{\mathrm{live}}$ to reflect the current state of the proposal $\tilde{p}(\mathbf z)$; and b) a training/inference process where a posterior estimate $q_\phi$ is optimised on the current state of the dataset $\mathcal{D}_{\mathrm{live}}$, and the proposal $\tilde{p}$ is subsequently updated to sequentially target some observed data ${\mathbf x_\text{obs}}$. These two processes run in parallel, and communicate via a set of shared resources, which includes the live dataset $\mathcal{D}_{\mathrm{live}}$, the parameter proposal $\tilde{p}(\mathbf z)$, and the observational data ${\mathbf x_\text{obs}}$.
• Figure \thealg: Algorithm -- Dynamic Simulation-Based Inference (DS)
• Figure \thealg: 10-D Bimodal Gaussian Mixture in DS-A: Results for the synthetic benchmark described in Section \ref{['example1']}. Left (corner plot): Comparison between reference samples from the target posterior (pink) and samples from the learned posterior (blue). Black dashed vertical lines and markers indicate the two mode locations in each dimension. Middle upper (loss): Training (green) and validation (red) losses versus epochs. Right upper (range): Evolution of the per-dimension training parameter range, shown as smoothed minimum (orange, solid) and maximum (purple, dashed) across mini-batches. Right lower (convergence): Dataset convergence during training, plotting $\lvert z_{\mathrm{extreme}}-z_{\mathrm{true}}\rvert$ per dimension (orange for minima, purple for maxima) on a log scale; the dotted black line marks the noise level.
• Figure \thealg: Comparison of DS-A, Round-based, and amortised methods.Left upper: Training (dashed) and validation (solid) losses versus elapsed time (minutes from the start) for four schemes: Dynamic SBI (blue), Amortised (pink), Round-based (keep old data; orange), and Round-based (only keep new data; green). Left lower: Cumulative number of simulations versus elapsed time for the same four schemes. Right four panels: Evolution of simulation identifiers over elapsed time for each scheme separately. In these panels, blue dots denote training simulations and magenta dots denote validation simulations.
• Figure \thealg: Stochastic Gravitational Wave Background: Analysis results for the SGWB case study presented in Section \ref{['sec:physics']}. Left corner plot: Comparison between the reference samples (pink) and samples from the learned posterior (blue) for the benchmark case study described in the main text. The true values of the injection parameters are shown with dotted black lines and dots. Right upper: The training (blue) and validation (pink) losses as a function of the number of training epochs. Right middle: The total simulation count (across training and validation) used in the training run. Right lower: The observation data analysed in this case study from the three different (A, E, and T) data channels.