In this work, we introduce an open-source integrated CAD-CFD tool, Anvil, which combines FreeCAD for CAD modeling and OpenFOAM for CFD analysis, along with an AI-based optimization method (Bayesian optimization) and other sampling algorithms. Anvil serves as a scientific machine learning tool for shape optimization in three modes: data generation, CFD evaluation, and shape optimization. In data generation mode, it automatically runs CFD evaluations and generates data for training a surrogate model. In optimization mode, it searches for the optimal design under given requirements and optimization metrics. In CFD mode, a single CAD file can be evaluated with a single OpenFOAM run. To use Anvil, experimenters provide a JSON configuration file and a parametric CAD seed design. Anvil can be used to study solid-fluid dynamics for any subsonic flow conditions and has been demonstrated in various simulation and optimization use cases. The open-source code for the tool, installation process, artifacts (such as CAD seed designs and example STL models), experimentation results, and detailed documentation can be found at \url{https://github.com/symbench/Anvil}.

Although the finite element approach of the Ice-sheet and Sea-level System Model (ISSM) solves ice dynamics problems governed by Stokes equations quickly and accurately, such numerical modeling requires intensive computation on central processing units (CPU). In this study, we develop graph neural networks (GNN) as fast surrogate models to preserve the finite element structure of ISSM. Using the 20-year transient simulations in the Pine Island Glacier (PIG), we train and test three GNNs: graph convolutional network (GCN), graph attention network (GAT), and equivariant graph convolutional network (EGCN). These GNNs reproduce ice thickness and velocity with better accuracy than the classic convolutional neural network (CNN) and multi-layer perception (MLP). In particular, GNNs successfully capture the ice mass loss and acceleration induced by higher basal melting rates in the PIG. When our GNN emulators are implemented on graphic processing units (GPUs), they show up to 50 times faster computational time than the CPU-based ISSM simulation.

There are several numerical models that describe real phenomena being used to solve complex problems. For example, an accurate numerical breast model can provide assistance to surgeons with visual information of the breast as a result of a surgery simulation. The process of finding the model parameters requires numeric inputs, either based in medical imaging techniques, or other measures. Inputs can be processed by iterative methods (inverse elasticity solvers). Such solvers are highly robust and provide solutions within the required degree of accuracy. However, their computational complexity is costly. On the other hand, machine learning based approaches provide outputs in real-time. Although high accuracy rates can be achieved, these methods are not exempt from producing solutions outside the required degree of accuracy. In the context of real life situations, a non accurate solution might present complications to the patient. We present an hybrid parameter estimation method to take advantage of the positive features of each of the aforementioned approaches. Our method preserves both the real-time performance of deep-learning methods, and the reliability of inverse elasticity solvers. The underlying reasoning behind our proposal is the fact that deep-learning methods, such as neural networks, can provide accurate results in the majority of cases and they just need a fail-safe system to ensure its reliability. Hence, we propose using a Multilayer Neural Networks (MNN) to get an estimation which is in turn validated by a iterative solver. In case the MNN provides an estimation not within the required accuracy range, the solver refines the estimation until the required accuracy is achieved. Based on our results we can conclude that the presented hybrid method is able to complement the computational performance of MNNs with the robustness of iterative solver approaches.

Current system thermal-hydraulic codes have limited credibility in simulating real plant conditions, especially when the geometry and boundary conditions are extrapolated beyond the range of test facilities. This paper proposes a data-driven approach, Feature Similarity Measurement FFSM), to establish a technical basis to overcome these difficulties by exploring local patterns using machine learning. The underlying local patterns in multiscale data are represented by a set of physical features that embody the information from a physical system of interest, empirical correlations, and the effect of mesh size. After performing a limited number of high-fidelity numerical simulations and a sufficient amount of fast-running coarse-mesh simulations, an error database is built, and deep learning is applied to construct and explore the relationship between the local physical features and simulation errors. Case studies based on mixed convection have been designed for demonstrating the capability of data-driven models in bridging global scale gaps.

To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale framework was proposed in this paper by applying a physics-guided data-driven approach. Instrumental to this framework, Feature Similarity Measurement (FSM) technique was developed for error estimation in two-phase flow simulation using coarse-mesh CFD, to achieve a comparable accuracy as fine-mesh simulations with fast-running feature. By defining physics-guided parameters and variable gradients as physical features, FSM has the capability to capture the underlying local patterns in the coarse-mesh CFD simulation. Massive low-fidelity data and respective high-fidelity data are used to explore the underlying information relevant to the main simulation errors and the effects of phenomenological scaling. By learning from previous simulation data, a surrogate model using deep feedforward neural network (DFNN) can be developed and trained to estimate the simulation error of coarse-mesh CFD. The research documented supports the feasibility of the physics-guided deep learning methods for coarse mesh CFD simulations which has a potential for the efficient industrial design.

In this paper, we propose the use of a black-box optimization method called deterministic Mesh Adaptive Direct Search (MADS) algorithm with orthogonal directions (Ortho-MADS) for the selection of hyperparameters of Support Vector Machines with a Gaussian kernel. Different from most of the methods in the literature that exploit the properties of the data or attempt to minimize the accuracy of a validation dataset over the first quadrant of (C, gamma), the Ortho-MADS provides convergence proof. We present the MADS, followed by the Ortho-MADS, the dynamic stopping criterion defined by the MADS mesh size and two different search strategies (Nelder-Mead and Variable Neighborhood Search) that contribute to a competitive convergence rate as well as a mechanism to escape from undesired local minima. We have investigated the practical selection of hyperparameters for the Support Vector Machine with a Gaussian kernel, i.e., properly choose the hyperparameters gamma (bandwidth) and C (trade-off) on several benchmark datasets. The experimental results have shown that the proposed approach for hyperparameter tuning consistently finds comparable or better solutions, when using a common configuration, than other methods. We have also evaluated the accuracy and the number of function evaluations of the Ortho-MADS with the Nelder-Mead search strategy and the Variable Neighborhood Search strategy using the mesh size as a stopping criterion, and we have achieved accuracy that no other method for hyperparameters optimization could reach.

We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare these results with conventional derivative-free global search algorithms, such as (single-fidelity) Gaussian Processes optimization scheme, and Particle Swarm Optimization---a commonly used method in nanophotonics community, which is implemented in Lumerical commercial photonics software. We demonstrate the performance of various numerical optimization approaches on several pre-collected real-world datasets and show that by properly trading off expensive information sources with cheap simulations, one can more effectively optimize the transmission properties with a fixed budget.