Learning Generative Models with Sinkhorn Divergences

The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the estimation of generative models for high-dimensional observations such as those arising in computer vision or natural language. It is known that optimal transport metrics can represent a cure for this problem, since they were specifically designed as an alternative to information divergences to handle such problematic scenarios. Unfortunately, training generative machines using OT raises formidable computational and statistical challenges, because of (i) the computational burden of evaluating OT losses, (ii) the instability and lack of smoothness of these losses, (iii) the difficulty to estimate robustly these losses and their gradients in high dimension. This paper presents the first tractable computational method to train large scale generative models using an optimal transport loss, and tackles these three issues by relying on two key ideas: (a) entropic smoothing, which turns the original OT loss into one that can be computed using Sinkhorn fixed point iterations; (b) algorithmic (automatic) differentiation of these iterations. These two approximations result in a robust and differentiable approximation of the OT loss with streamlined GPU execution. Entropic smoothing generates a family of losses interpolating between Wasserstein (OT) and Maximum Mean Discrepancy (MMD), thus allowing to find a sweet spot leveraging the geometry of OT and the favorable high-dimensional sample complexity of MMD which comes with unbiased gradient estimates. The resulting computational architecture complements nicely standard deep network generative models by a stack of extra layers implementing the loss function

Automated transition state theory calculations for high-throughput kinetics

A scarcity of known chemical kinetic parameters leads to the use of many reaction rate estimates, which are not always sufficiently accurate, in the construction of detailed kinetic models. To reduce the reliance on these estimates and improve the accuracy of predictive kinetic models, we have developed a high-throughput, fully automated, reaction rate calculation method, AutoTST. The algorithm integrates automated saddle-point geometry search methods and a canonical transition state theory kinetics calculator. The automatically calculated reaction rates compare favorably to existing estimated rates. Comparison against high level theoretical calculations show the new automated method performs better than rate estimates when the estimate is made by a poor analogy. The method will improve by accounting for internal rotor contributions and by improving methods to determine molecular symmetry.Comment: 29 pages, 8 figure

Wake dynamics and rotor-fuselage aerodynamic interactions

The unsteady loads experienced by a helicopter are known to be strongly influenced by aerodynamic interactions between the rotor and fuselage; these unsteady loads can lead to deficiencies in handling qualities and unacceptable vibratory characteristics of the rotorcraft. This work uses a vorticity-based computational model to study the governing processes that underpin this aerodynamic interaction and aims to provide greater understanding of the wake dynamics in the presence of a fuselage, as well as an appreciation of how the geometry of the wake affects the loading on the fuselage. The well-known experiments using NASA's ROBIN fuselage are used to assess the accuracy of the computations. Comparisons of calculations against results from smoke visualization experiments are used to demonstrate the ability of the model to reproduce accurately the geometry of the rotor wake, and comparisons with inflow data from the experiments show the method to capture well the velocity field near to the rotor. The fuselage model is able to predict accurately the unsteady fuselage loading that is induced by blade passage and also by the inviscid interaction between the main rotor wake and fuselage

Aerodynamics of aero-engine installation

This paper describes current progress in the development of methods to assess aero-engine airframe installation effects. The aerodynamic characteristics of isolated intakes, a typical transonic transport aircraft as well as a combination of a through-flow nacelle and aircraft configuration have been evaluated. The validation task for an isolated engine nacelle is carried out with concern for the accuracy in the assessment of intake performance descriptors such as mass flow capture ratio and drag rise Mach number. The necessary mesh and modelling requirements to simulate the nacelle aerodynamics are determined. Furthermore, the validation of the numerical model for the aircraft is performed as an extension of work that has been carried out under previous drag prediction research programmes. The validation of the aircraft model has been extended to include the geometry with through flow nacelles. Finally, the assessment of the mutual impact of the through flow nacelle and aircraft aerodynamics was performed. The drag and lift coefficient breakdown has been presented in order to identify the component sources of the drag associated with the engine installation. The paper concludes with an assessment of installation drag for through-flow nacelles and the determination of aerodynamic interference between the nacelle and the aircraft