Background: The positive predictive value (PPV) of large language model (LLM)-based proofreading for radiology reports is limited due to the low error prevalence. Purpose: To assess whether a three-pass LLM framework enhances PPV and reduces operational costs compared with baseline approaches. Materials and Methods: A retrospective analysis was performed on 1,000 consecutive radiology reports (250 each: radiography, ultrasonography, CT, MRI) from the MIMIC-III database. Two external datasets (CheXpert and Open-i) were validation sets. Three LLM frameworks were tested: (1) single-prompt detector; (2) extractor plus detector; and (3) extractor, detector, and false-positive verifier. Precision was measured by PPV and absolute true positive rate (aTPR). Efficiency was calculated from model inference charges and reviewer remuneration. Statistical significance was tested using cluster bootstrap, exact McNemar tests, and Holm-Bonferroni correction. Results: Framework PPV increased from 0.063 (95% CI, 0.036-0.101, Framework 1) to 0.079 (0.049-0.118, Framework 2), and significantly to 0.159 (0.090-0.252, Framework 3; P<.001 vs. baselines). aTPR remained stable (0.012-0.014; P>=.84). Operational costs per 1,000 reports dropped to USD 5.58 (Framework 3) from USD 9.72 (Framework 1) and USD 6.85 (Framework 2), reflecting reductions of 42.6% and 18.5%, respectively. Human-reviewed reports decreased from 192 to 88. External validation supported Framework 3's superior PPV (CheXpert 0.133, Open-i 0.105) and stable aTPR (0.007). Conclusion: A three-pass LLM framework significantly enhanced PPV and reduced operational costs, maintaining detection performance, providing an effective strategy for AI-assisted radiology report quality assurance.

In this paper we introduce a numerical method for parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the subproblems is comparatively small, the approach can handle extremely high-dimensional PDEs. We test the method on different examples from physics, stochastic control, and mathematical finance. In all cases, it yields very good results in up to 10,000 dimensions with short run times.

High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, transaction costs, volatility uncertainty (Knightian uncertainty), or trading constraints in the model. Such high-dimensional fully nonlinear PDEs are exceedingly difficult to solve as the computational effort for standard approximation methods grows exponentially with the dimension. In this work we propose a new method for solving high-dimensional fully nonlinear second-order PDEs. Our method can in particular be used to sample from high-dimensional nonlinear expectations. The method is based on (i) a connection between fully nonlinear second-order PDEs and second-order backward stochastic differential equations (2BSDEs), (ii) a merged formulation of the PDE and the 2BSDE problem, (iii) a temporal forward discretization of the 2BSDE and a spatial approximation via deep neural nets, and (iv) a stochastic gradient descent-type optimization procedure. Numerical results obtained using ${\rm T{\small ENSOR}F{\small LOW}}$ in ${\rm P{\small YTHON}}$ illustrate the efficiency and the accuracy of the method in the cases of a $100$-dimensional Black-Scholes-Barenblatt equation, a $100$-dimensional Hamilton-Jacobi-Bellman equation, and a nonlinear expectation of a $ 100 $-dimensional $ G $-Brownian motion.