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Chess endgame tables encode unapproximated game- theoretic values of endgame positions. The speed at which information is retrieved from these tables and their representation size are major limiting factors in their effective use. We explore and make novel extensions to three alternatives (decision trees, decision diagrams, and logic minimization) to the currently preferred implementation (Syzygy) for representing such tables. Syzygy is most compact, but also slowest at handling queries. Two-level logic minimization works well when the full compression algorithm can be run. Decision DAGs and multiterminal binary decision diagrams are comparable and offer the best querying times, with decision diagrams providing better compression. 

Chess endgame tables encode unapproximated game-theoretic values of endgame positions. The speed at which information is retrieved from these tables and their representation size are major limiting factors in their effective use. We explore and make novel extensions to three alternatives (decision trees, decision diagrams, and logic minimization) to the currently preferred implementation (Syzygy) for representing such tables. Syzygy is most compact, but also slowest at handling queries. Two-level logic minimization works well, though performing the compression takes significant time. Decision DAGs and multiterminal binary decision diagrams are both comparable and offer the best querying times, with decision diagrams providing better compression. 

Abstract We present methods for emulating the matter power spectrum by combining information from cosmological N-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter space of a limited number of simulations. We present the first implementation in cosmology of multi-fidelity emulation, where many low-resolution simulations are combined with a few high-resolution simulations to achieve an increased emulation accuracy. The power spectrum’s dependence on cosmology is learned from the low-resolution simulations, which are in turn calibrated using high-resolution simulations. We show that our multi-fidelity emulator predicts high-fidelity counterparts to percent-level relative accuracy when using only 3 high-fidelity simulations and outperforms a single-fidelity emulator that uses 11 simulations, although we do not attempt to produce a converged emulator with high absolute accuracy. With a fixed number of high-fidelity training simulations, we show that our multi-fidelity emulator is ≃ 100 times better than a single-fidelity emulator at k ≤ 2 hMpc−1, and ≃ 20 times better at 3 ≤ k < 6.4 hMpc−1. Multi-fidelity emulation is fast to train, using only a simple modification to standard Gaussian processes. Our proposed emulator shows a new way to predict non-linear scales by fusing simulations from different fidelities. 

Inverse problems continue to garner immense interest in the physical sciences, particularly in the context of controlling desired phenomena in non-equilibrium systems. In this work, we utilize a series of deep neural networks for predicting time-dependent optimal control fields, E ( t ), that enable desired electronic transitions in reduced-dimensional quantum dynamical systems. To solve this inverse problem, we investigated two independent machine learning approaches: (1) a feedforward neural network for predicting the frequency and amplitude content of the power spectrum in the frequency domain ( i.e. , the Fourier transform of E ( t )), and (2) a cross-correlation neural network approach for directly predicting E ( t ) in the time domain. Both of these machine learning methods give complementary approaches for probing the underlying quantum dynamics and also exhibit impressive performance in accurately predicting both the frequency and strength of the optimal control field. We provide detailed architectures and hyperparameters for these deep neural networks as well as performance metrics for each of our machine-learned models. From these results, we show that machine learning, particularly deep neural networks, can be employed as cost-effective statistical approaches for designing electromagnetic fields to enable desired transitions in these quantum dynamical systems. 

ABSTRACT We develop an automated technique to measure quasar redshifts in the Baryon Oscillation Spectroscopic Survey of the Sloan Digital Sky Survey (SDSS). Our technique is an extension of an earlier Gaussian process method for detecting damped Lyman α absorbers (DLAs) in quasar spectra with known redshifts. We apply this technique to a subsample of SDSS DR12 with BAL quasars removed and redshift larger than 2.15. We show that we are broadly competitive to existing quasar redshift estimators, disagreeing with the PCA redshift by more than 0.5 in only $$0.38{{\ \rm per\ cent}}$$ of spectra. Our method produces a probabilistic density function for the quasar redshift, allowing quasar redshift uncertainty to be propagated to downstream users. We apply this method to detecting DLAs, accounting in a Bayesian fashion for redshift uncertainty. Compared to our earlier method with a known quasar redshift, we have a moderate decrease in our ability to detect DLAs, predominantly in the noisiest spectra. The area under curve drops from 0.96 to 0.91. Our code is publicly available.