Physical Simulators as Do-Operators: Causal Discovery under Latent Confounders for AI-for-Science

We propose SVAR-FM (Structural VAR with Flow Matching), a framework for time series causal discovery that treats a physics-based simulator as a mechanical realization of Pearl's do operator. Clamping a variable inside the simulator physically severs confounding paths, producing interventional data by construction. Conditional Flow Matching then learns the nonlinear interventional conditionals. Theoretically, we prove that the full structural VAR becomes identifiable under a coverage condition on the simulator-clampable variables, and derive an end-to-end error bound that decomposes into Monte Carlo, simulator fidelity, and Flow Matching terms. A sign-flip corollary predicts that when simulator accuracy falls below a threshold, the estimated causal effect reverses sign. Empirically, a benchmark across four scientific domains confirms that SVAR-FM recovers the correct causal sign where observational methods produce sign-reversed estimates due to confounding. A case study in ultrafast laser physics verifies the sign-flip prediction by physically varying the accuracy level of a first-principles quantum solver: the low-accuracy setting reverses the causal sign, while the high-accuracy setting recovers the correct direction (R-squared = 0.983, zero bias).

We introduce CausaLab, a scalable environment for evaluating interactive causal discovery by LLM agents. Unlike prior evaluations, CausaLab evaluates both whether an agent can solve a problem using causal evidence and whether its answer is grounded in a faithful recovered causal mechanism. Each episode places an agent in a synthetic laboratory: it receives prior measurement records, intervenes on a manipulator crystal, and predicts the resonance frequency of a held-out reactor crystal governed by the same mechanism. The hidden data-generating process is a randomly sampled structural causal model (SCM), so success requires recovering both a causal graph and structural equations rather than recalling prior knowledge. Experiments show a persistent gap between prediction and mechanism recovery: in the purely observational 6-node setting, GPT-5.2-high reaches 92% task accuracy but only 0.471 all-edge $F_1$. Mixed observation-intervention strategies improve structural fidelity, while pure intervention remains difficult even for strong agents. We identify premature stopping as a major weakness and show that consistency verification mitigates it. CausaLab therefore separates predictive success from causal understanding and exposes current LLM agents' limits as experimental causal reasoners.

Causal discovery from observational data remains challenging due to the need to recover directed structure and latent confounding without interventions. We propose FoundCause, an amortized causal discovery model trained entirely on synthetic data that maps datasets directly to causal graphs in a single forward pass. By learning from large collections of simulated structural causal models, FoundCause captures transferable statistical patterns that generalize beyond individual datasets. The architecture incorporates several key inductive biases for causal discovery. It uses a permutation-invariant transformer encoder with alternating attention over samples and variables to jointly model cross-variable dependence and per-variable distributions. Pairwise statistical features derived from classical asymmetry measures are injected through statistics-conditioned attention, guiding the model toward known causal signals. A factorized decoder separates edge existence from direction, while a triangular refinement module enables reasoning over higher-order causal motifs such as chains and colliders. In addition, a dedicated confounder module based on learnable latent tokens explicitly models hidden common causes, and the model explicitly handles missing data via its masked input representation. To our knowledge, FoundCause is the first amortized causal discovery approach to explicitly model latent confounding. FoundCause outperforms 11 classical non-amortized methods (e.g., PC, GES, NOTEARS-style optimization) and 4 amortized causal discovery methods on 15 real-world datasets, achieving +9.6% improvement in $F_1$, +1.2% in AUROC, and an 18.9% reduction in structural Hamming distance relative to the strongest non-amortized methods, while performing inference in a single forward pass.