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The show exists in a strange world where men repeatedly confess their love for each other. Does it make them better people? Much ink has been spilled, and countless TikToks recorded, in an effort to explain the female fervor unleashed by the series " Heated Rivalry ." I, a thirty-eight-year-old woman who owns a T-shirt that bears the logo of Shane Hollander's Montreal Metros and another that celebrates Ilya Rozanov's Boston Raiders (Valentine's Day gifts, it should be said, from my indulgent husband), don't find its appeal so mystifying. Two gorgeous young men, as elegantly muscled as Myron's discus thrower, have ecstatically unbridled, mutually satisfying sex to a soundtrack designed to tickle elder millennials' nostalgia-pleasure centers, all while falling in the kind of soul-sustaining love that most of us can only dream of.

Parametric stochastic simulators are ubiquitous in science, often featuring highdimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural simulation-based inference algorithm which simultaneously offers simulation efficiency and fast empirical posterior testability, which is unique among modern algorithms. Our approach is simulation efficient by simultaneously estimating low-dimensional marginal posteriors instead of the joint posterior and by proposing simulations targeted to an observation of interest via a prior suitably truncated by an indicator function. Furthermore, by estimating a locally amortized posterior our algorithm enables efficient empirical tests of the robustness of the inference results. Since scientists cannot access the ground truth, these tests are necessary for trusting inference in real-world applications. We perform experiments on a marginalized version of the simulation-based inference benchmark and two complex and narrow posteriors, highlighting the simulator efficiency of our algorithm as well as the quality of the estimated marginal posteriors.

Physics-informed neural networks (PINNs) are neural networks trained by using physical laws in the form of partial differential equations (PDEs) as soft constraints. We present a new technique for the accelerated training of PINNs that combines modern scientific computing techniques with machine learning: discretely-trained PINNs (DT-PINNs). The repeated computation of the partial derivative terms in the PINN loss functions via automatic differentiation during training is known to be computationally expensive, especially for higher-order derivatives. DT-PINNs are trained by replacing these exact spatial derivatives with high-order accurate numerical discretizations computed using meshless radial basis function-finite differences (RBF-FD) and applied via sparse-matrix vector multiplication. While in principle any high-order discretization may be used, the use of RBF-FD allows for DT-PINNs to be trained even on point cloud samples placed on irregular domain geometries.