New biological assays like Perturb-seq link highly parallel CRISPR interventions to a high-dimensional transcriptomic readout, providing insight into gene regulatory networks. Causal gene regulatory networks can be represented by directed acyclic graph (DAGs), but learning DAGs from observational data is complicated by lack of identifiability and a combinatorial solution space. Score-based structure learning improves practical scalability of inferring DAGs. Previous score-based methods are sensitive to error variance structure; on the other hand, estimation of error variance is difficult without prior knowledge of structure. Accordingly, we present $\texttt{dotears}$ [doo-tairs], a continuous optimization framework which leverages observational and interventional data to infer a single causal structure, assuming a linear Structural Equation Model (SEM). $\texttt{dotears}$ exploits structural consequences of hard interventions to give a marginal estimate of exogenous error structure, bypassing the circular estimation problem. We show that $\texttt{dotears}$ is a provably consistent estimator of the true DAG under mild assumptions. $\texttt{dotears}$ outperforms other methods in varied simulations, and in real data infers edges that validate with higher precision and recall than state-of-the-art methods through differential expression tests and high-confidence protein-protein interactions.

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