Physically Interpretable Probabilistic Domain Characterization

Characterizing domains is essential for models analyzing dynamic environments, as it allows them to adapt to evolving conditions or to hand the task over to backup systems when facing conditions outside their operational domain. Existing solutions typically characterize a domain by solving a regression or classification problem, which limits their applicability as they only provide a limited summarized description of the domain. In this paper, we present a novel approach to domain characterization by characterizing domains as probability distributions. Particularly, we develop a method to predict the likelihood of different weather conditions from images captured by vehicle-mounted cameras by estimating distributions of physical parameters using normalizing flows. To validate our proposed approach, we conduct experiments within the context of autonomous vehicles, focusing on predicting the distribution of weather parameters to characterize the operational domain. This domain is characterized by physical parameters (absolute characterization) and arbitrarily predefined domains (relative characterization). Finally, we evaluate whether a system can safely operate in a target domain by comparing it to multiple source domains where safety has already been established. This approach holds significant potential, as accurate weather prediction and effective domain adaptation are crucial for autonomous systems to adjust to dynamic environmental conditions.

💡 Research Summary

The paper tackles the problem of domain characterization for autonomous driving systems operating under varying weather conditions. Traditional approaches treat domain characterization as a regression or classification task, yielding a single deterministic estimate of the environment (e.g., “rainy” or a point estimate of cloudiness). Such methods ignore the inherent ambiguity that a single camera image can correspond to many plausible weather states. To overcome this limitation, the authors propose a fundamentally probabilistic framework: a domain is represented by a probability distribution over physical parameters (weather variables), and the task becomes estimating this distribution from visual observations.

The core technical contribution is the use of normalizing flows—specifically Neural Spline Flows (NSF)—within a Simulation‑Based Inference (SBI) pipeline. Normalizing flows provide a bijective mapping between a simple base distribution (e.g., a multivariate Gaussian) and a complex target distribution, enabling both density evaluation and efficient sampling. By training a Neural Posterior Estimation (NPE) model on a large synthetic dataset generated with the CARLA driving simulator, the system learns to map an input image to the posterior distribution P(W | I=i), where W denotes a six‑dimensional vector of weather parameters (cloudiness, fog density, precipitation, sun altitude, wind intensity, precipitation deposits) and I is the captured front‑view image.

The dataset comprises 635 k images with uniformly sampled weather parameters; 600 k images are used for training/validation, and 35 k for testing. Feature extraction is performed with frozen backbones (ResNet‑50, DINOv2, CLIP), after which the features are fed into the flow model. The authors evaluate the learned posteriors using several established SBI diagnostics: marginal histograms, corner plots (showing pairwise joint densities and credibility regions), coverage plots (to assess calibration), and Posterior Predictive Checks (PPC) where sampled weather parameters are re‑injected into CARLA to generate synthetic images that are compared with the original observation.

Results demonstrate that the model captures substantial uncertainty—most marginal distributions are wide, reflecting the fact that a single image rarely determines weather uniquely. Nevertheless, the credible regions are interpretable, and the PPC confirms that sampled parameters produce realistic images. The authors also explore two extensions beyond the basic “absolute” characterization. First, they aggregate predictions over a bag of images to obtain a more robust domain estimate. Second, they introduce a “relative” characterization: given a target domain, they compare its posterior to a set of pre‑defined source domains (e.g., clear, rainy, foggy) by measuring KL‑divergence between the respective flow models. This allows a system to decide whether it is operating within a known safe Operational Design Domain (ODD) as defined by SAE, by checking if the target domain can be expressed as a mixture of previously validated source domains.

The paper’s contributions are threefold: (1) a novel probabilistic methodology for domain characterization in autonomous driving, (2) demonstration that normalizing flows are suitable for high‑dimensional image‑to‑parameter inference, and (3) a framework for safety assessment via mixture modeling of source domains. Limitations include reliance on synthetic data, computational cost of processing high‑resolution features through flows, and the current focus on RGB images only. Future work is suggested on domain adaptation to real‑world data, lightweight flow architectures, and multimodal fusion with lidar or radar.

Overall, the study provides a compelling argument for moving from deterministic to distributional domain descriptions, offering a principled way to quantify uncertainty, improve interpretability, and integrate domain characterization directly into safety verification pipelines for autonomous vehicles.