We study nonparametric contextual bandits under batch constraints, where the expected reward for each action is modeled as a smooth function of covariates, and the policy updates are made at the end of each batch of o...
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We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold Brownian Incremen...
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We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained o...
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We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.
Entropy stable discontinuous Galerkin (DG) methods improve the robustness of high order DG simulations of nonlinear conservation laws. These methods yield a semi-discrete entropy inequality, and rely on an algebraic f...
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We derive global estimates for the error in solutions of linear hyperbolic systems due to inaccurate boundary geometry. We show that the error is bounded by data and bounded in time when the solutions in the true and ...
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We propose P-order (Power-order), a unified, norm-independent framework for quantifying the convergence rates of iterative methods. Standard analyses based on Q-order are norm-dependent and require some uniformity of ...
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Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interes...
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Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interest using minimal quantum resources. In this work, we will use eigenvector continuation to build a subspace from the low-lying states of a set of Hamiltonians. The basis vectors are prepared using truncated versions of standard state preparation methods such as imaginary-time evolution (ITE), adiabatic state preparation (ASP), and variational quantum eigensolver. By using these truncated methods combined with eigenvector continuation, we can directly improve upon them, obtaining more accurate ground-state energies at a reduced cost. We use several spin systems to demonstrate convergence even when methods like ITE and ASP fail, such as ASP in the presence of level crossings and ITE with vanishing energy gaps. We also showcase the noise resilience of this approach beyond the gains already made by having shallower quantum circuits. Our findings suggest that eigenvector continuation can be used to improve existing state preparation methods in the near term.
Modern financial networks involve complex obligations that transcend simple monetary debts: multiple currencies, prioritized claims, supply chain dependencies, and more. We present a mathematical framework that unifie...
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We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincaré–Steklov (HPS)...
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