Curry-style type Isomorphisms and Game Semantics

Curry-style system F, ie. system F with no explicit types in terms, can be seen as a core presentation of polymorphism from the point of view of programming languages. This paper gives a characterisation of type isomorphisms for this language, by using a game model whose intuitions come both from the syntax and from the game semantics universe. The model is composed of: an untyped part to interpret terms, a notion of game to interpret types, and a typed part to express the fact that an untyped strategy plays on a game. By analysing isomorphisms in the model, we prove that the equational system corresponding to type isomorphisms for Curry-style system F is the extension of the equational system for Church-style isomorphisms with a new, non-trivial equation: forall X.A = A[forall Y.Y/X] if X appears only positively in A.Comment: Accept\'e \`a Mathematical Structures for Computer Science, Special Issue on Type Isomorphism

Second-Order Type Isomorphisms Through Game Semantics

The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λ$\mu$-calculus, which can be seen as an extension of system F to classical logic, and for which we define a categorical framework: control hyperdoctrines. Our game model of λ$\mu$-calculus is based on polymorphic arenas (closely related to Hughes' hyperforests) which evolve during the play (following the ideas of Murawski-Ong). We show that type isomorphisms coincide with the "equality" on arenas associated with types. Finally we deduce the equational characterization of type isomorphisms from this equality. We also recover from the same model Roberto Di Cosmo's characterization of type isomorphisms for system F. This approach leads to a geometrical comprehension on the question of second order type isomorphisms, which can be easily extended to some other polymorphic calculi including additional programming features.Comment: accepted by Annals of Pure and Applied Logic, Special Issue on Game Semantic

Deep Deterministic Portfolio Optimization

Can deep reinforcement learning algorithms be exploited as solvers for optimal trading strategies? The aim of this work is to test reinforcement learning algorithms on conceptually simple, but mathematically non-trivial, trading environments. The environments are chosen such that an optimal or close-to-optimal trading strategy is known. We study the deep deterministic policy gradient algorithm and show that such a reinforcement learning agent can successfully recover the essential features of the optimal trading strategies and achieve close-to-optimal rewards.Comment: Minor typ

Advanced Wave Generation Systems for Numerical Modelling of Coastal Structures

Accurate generation of wave climates in the context of numerical models (and in particular CFD models) is a challenging problem, as these are increasingly used to provide design support to coastal engineering projects. In this paper we will briefly present a technique that addresses the generation (and active absorption) of non-repeating wave sequences for modelling storm events in a meaningful manner. This technique includes a spectral window preprocessing method that is used to reduce the computational costs associated with wave generation algorithms. These can be particularly cumbersome for generating storm events. It was demonstrated that numerical cost can be reduced by about 40 times by using O(101) frequencies for wave reconstruction, rather than O(104) which current methods would need to accurately reproduce long wave series, without any noticeable difference in terms of the generated wave signal. The technique is already in use within the context of the computational toolkit Proteus (https://github.com/erdc/proteus) and is it is combined with both the CFD and shallow water module of the model. The methodology is also fit with a 2nd order correction for generating nonlinear random wave series. Case studies are also presented that prove i) the capability of the technique to reproduce meaningful sea states in the context of numerical modelling of coastal structures and ii) the improvement of computational cost, when compared to currently available techniques. These case studies comprise modelling of random waves in a numerical wave tank to acquire wave statistics by using both CFD and shallow water models, as well as modelling coastal structures such as a low-crested levees and a caisson breakwater using random sea states

High-fidelity computational modelling of fluid–structure interaction for moored floating bodies

The development and implementation process of a complete numerical framework for high-fidelity Fluid–Structure Interaction (FSI) simulations of moored floating bodies using Computational Fluid Dynamics (CFD) with the Finite Element Method (FEM) is presented here. For this purpose, the following three main aspects are coupled together: Two-Phase Flow (TPF), Multibody Dynamics (MBD), and mooring dynamics. The fluid–structure problem is two-way and fully partitioned, allowing for high modularity of the coupling and computational efficiency. The Arbitrary Lagrangian–Eulerian (ALE) formulation is used for describing the motion of the mesh-conforming fluid–solid interface, and mesh deformation is achieved with linear elastostatics. Mooring dynamics is performed using gradient deficient Absolute Nodal Coordinate Formulation (ANCF) elements with a two-way mooring–structure coupling and a one-way fluid–mooring coupling. Hydrodynamic loads are applied accurately along mooring cables using the solution of the fluid velocity provided by the TPF solver. For this purpose, fluid mesh elements containing cable nodes that do not conform to the fluid mesh are located with a computationally efficient particle-localisation algorithm. As it is common for partitioned FSI simulations of solids moving within a relatively dense fluid to experience unconditional instability from the added mass effect in CFD, a non-iterative stabilisation scheme is developed here. This is achieved with an accurate and dynamic estimation of the added mass for arbitrarily shaped structures that is then applied as a penalty term to the equations of motion of the solid. It is shown that this stabilisation scheme ensures stability of FSI simulations that are otherwise prone to strong added mass effect without affecting the expected response of structures significantly, even when using fully partitioned fluid–structure coupling schemes. Thorough verification and validation for all aspects of the FSI framework ultimately show that the produced numerical results are in good agreement with experimental data and other inherently stable numerical models, even when complex nonlinear events occur such as vortices forming around sharp corners or extreme wave loads and overtopping on moving structures. It is also shown that the mooring dynamics model can successfully reproduce nonlinearities from high frequency fairlead motions and hydrodynamic loads. The large-scale 3D simulation of a floating semi-submersible structure moored with three catenary lines ties all the models and tools developed here together and shows the capability of the high-fidelity FSI framework to model complex systems robustly and accurately

CFD Modelling coupled with Floating Structures and Mooring Dynamics for Offshore Renewable Energy Devices using the Proteus Simulation Toolkit

This is the author accepted manuscript. The final version is available from EWTEC via the link in this record.In this work, the coupling of novel opensource tools for simulating two-phase incompressible flow problems with fluid-structure interaction and mooring dynamics is presented. The open-source Computational Fluid Dynamics (CFD) toolkit Proteus is used for the simulations. Proteus solves the twophase Navier-Stokes equations using the Finite Element Method (FEM) and is fully coupled with an Arbitrary Lagrangian-Eulerian (ALE) formulation for mesh motion allowing solid body motion within the fluid domain. The multi-body dynamics solver, Chrono, is used for calculating rigid body motion and modelling dynamics of complex mooring systems. At each time step, Proteus computes the forces from the fluid acting on the rigid body necessary to find its displacement with Chrono which will be used as boundary conditions for mesh motion. Several verification and validation cases are presented here in order to prove the successful coupling between the two toolkits aforementioned. These test cases include wave sloshing in a tank, floating body dynamics under free and wave-induced motion for different degrees of freedom (DOFs), and mooring dynamics using beam element theory coupled with rigid body dynamics and collision detection. The successful validation of each component shows the potential of the coupled methodology to be used for assisting the design of offshore renewable energy devices.Support for this work was given by the Engineer Research and Development Center (ERDC) and HR Wallingford through the collaboration agreement (Contract No. W911NF-15-2-0110). The authors also acknowledge support for the IDCORE program from the Energy Technologies Institute and the Research Councils Energy Programme (grant number EP/J500847/)

Fast random wave generation in numerical tanks

Generating and absorbing random waves in numerical models is a challenging problem, in particular when meaningful wave statistics should be generated to meet design sea state requirements. The methodology presented herein allows for the generation of random wave fields (free surface elevation and velocities) to be reconstructed in time and in space by using window processing from a reference time series