# Simultaneous identification of models and parameters of scientific simulators

arXiv: https://arxiv.org/abs/2305.15174 · HTML: https://mlsanity.com/paper/2305.15174/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 69 references that are in the map.
- First posted on arXiv 24 May 2023.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks](https://mlsanity.com/paper/1802.06153/) (2018)
- [Diagnostics for Conditional Density Models and Bayesian Inference Algorithms](https://mlsanity.com/paper/2102.10473/) (2021)
- [Amortized Bayesian model comparison with evidential deep learning](https://mlsanity.com/paper/2004.10629/) (2020)
- [Group equivariant neural posterior estimation](https://mlsanity.com/paper/2111.13139/) (2021)
- [Informed Equation Learning](https://mlsanity.com/paper/2105.06331/) (2021)
- [Simulation-based Bayesian inference for multi-fingered robotic grasping](https://mlsanity.com/paper/2109.14275/) (2021)
- [Efficient identification of informative features in simulation-based inference](https://mlsanity.com/paper/2210.11915/) (2022)
- [Discovering ordinary differential equations that govern time-series](https://mlsanity.com/paper/2211.02830/) (2022)
- [Multivariate binary probability distribution in the Grassmann formalism](https://mlsanity.com/paper/2009.08482/) (2020)

## Built on by (most cited first, 8 of 8)

- [Marrying Causal Representation Learning with Dynamical Systems for Science](https://mlsanity.com/paper/2405.13888/) (2024)
- [Consistency Models for Scalable and Fast Simulation-Based Inference](https://mlsanity.com/paper/2312.05440/) (2023)
- [Sensitivity-Aware Amortized Bayesian Inference](https://mlsanity.com/paper/2310.11122/) (2023)
- [A Probabilistic Framework for LLM-Based Model Discovery](https://mlsanity.com/paper/2602.18266/) (2026)
- [Improving the Accuracy of Amortized Model Comparison with Self-Consistency](https://mlsanity.com/paper/2508.20614/) (2025)
- [Amortized Bayesian Mixture Models](https://mlsanity.com/paper/2501.10229/) (2025)
- [Scalable Simulation-Based Model Inference with Test-Time Complexity Control](https://mlsanity.com/paper/2603.15292/) (2026)
- [Mixed neural posterior estimation for simulators with discrete and continuous parameters](https://mlsanity.com/paper/2605.13551/) (2026)

## Abstract (arXiv)

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.