# Model-based Validation as Probabilistic Inference

arXiv: https://arxiv.org/abs/2305.09930 · HTML: https://mlsanity.com/paper/2305.09930/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 17 May 2023.

## Builds on (most cited first, 13 of 13)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Self-Driving Cars: A Survey](https://mlsanity.com/paper/1901.04407/) (2019)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [Scalable End-to-End Autonomous Vehicle Testing via Rare-event Simulation](https://mlsanity.com/paper/1811.00145/) (2018)
- [Adaptive Stress Testing for Autonomous Vehicles](https://mlsanity.com/paper/1902.01909/) (2019)
- [A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical Systems](https://mlsanity.com/paper/2005.02979/) (2020)
- [Neural Bridge Sampling for Evaluating Safety-Critical Autonomous Systems](https://mlsanity.com/paper/2008.10581/) (2020)
- [Adaptive Stress Testing with Reward Augmentation for Autonomous Vehicle Validation](https://mlsanity.com/paper/1908.01046/) (2019)
- [Efficient Black-box Assessment of Autonomous Vehicle Safety](https://mlsanity.com/paper/1912.03618/) (2019)
- [Falsification of Cyber-Physical Systems Using Deep Reinforcement Learning](https://mlsanity.com/paper/1805.00200/) (2018)
- [Scalable Autonomous Vehicle Safety Validation through Dynamic Programming and Scene Decomposition](https://mlsanity.com/paper/2004.06801/) (2020)

## Built on by (most cited first, 3 of 3)

- [Diffusion-Based Failure Sampling for Evaluating Safety-Critical Autonomous Systems](https://mlsanity.com/paper/2406.14761/) (2024)
- [Rare event modeling with self-regularized normalizing flows: what can we learn from a single failure?](https://mlsanity.com/paper/2502.21110/) (2025)
- [Robust Planning for Autonomous Driving via Mixed Adversarial Diffusion Predictions](https://mlsanity.com/paper/2505.12327/) (2025)

## Abstract (arXiv)

Estimating the distribution over failures is a key step in validating autonomous systems. Existing approaches focus on finding failures for a small range of initial conditions or make restrictive assumptions about the properties of the system under test. We frame estimating the distribution over failure trajectories for sequential systems as Bayesian inference. Our model-based approach represents the distribution over failure trajectories using rollouts of system dynamics and computes trajectory gradients using automatic differentiation. Our approach is demonstrated in an inverted pendulum control system, an autonomous vehicle driving scenario, and a partially observable lunar lander. Sampling is performed using an off-the-shelf implementation of Hamiltonian Monte Carlo with multiple chains to capture multimodality and gradient smoothing for safe trajectories. In all experiments, we observed improvements in sample efficiency and parameter space coverage compared to black-box baseline approaches. This work is open sourced.