Stochastic simulation models, while effective in capturing the dynamics of complex systems, are often too slow to run for real-time decision-making. Metamodeling techniques are widely used to learn the relationship between a summary statistic of the outputs (e.g., the mean or quantile) and the inputs of the simulator, so that it can be used in real time. However, this methodology requires the knowledge of an appropriate summary statistic in advance, making it inflexible for many practical situations. In this paper, we propose a new metamodeling concept, called generative metamodeling, which aims to construct a "fast simulator of the simulator". This technique can generate random outputs substantially faster than the original simulation model, while retaining an approximately equal conditional distribution given the same inputs. Once constructed, a generative metamodel can instantaneously generate a large amount of random outputs as soon as the inputs are specified, thereby facilitating the immediate computation of any summary statistic for real-time decision-making. Furthermore, we propose a new algorithm -- quantile-regression-based generative metamodeling (QRGMM) -- and study its convergence and rate of convergence. Extensive numerical experiments are conducted to investigate the empirical performance of QRGMM, compare it with other state-of-the-art generative algorithms, and demonstrate its usefulness in practical real-time decision-making.

Generative adversarial networks (GANs) are one of the most robust and versatile techniques in the field of generative artificial intelligence. In this work, we report on an application of GANs in the domain of synthetic spectral data generation, offering a solution to the scarcity of data found in various scientific contexts. We demonstrate the proposed approach by applying it to an illustrative problem within the realm of near-field radiative heat transfer involving a multilayered hyperbolic metamaterial. We find that a successful generation of spectral data requires two modifications to conventional GANs: (i) the introduction of Wasserstein GANs (WGANs) to avoid mode collapse, and, (ii) the conditioning of WGANs to obtain accurate labels for the generated data. We show that a simple feed-forward neural network (FFNN), when augmented with data generated by a CWGAN, enhances significantly its performance under conditions of limited data availability, demonstrating the intrinsic value of CWGAN data augmentation beyond simply providing larger datasets. In addition, we show that CWGANs can act as a surrogate model with improved performance in the low-data regime with respect to simple FFNNs. Overall, this work highlights the potential of generative machine learning algorithms in scientific applications beyond image generation and optimization.

The solution of probabilistic inverse problems for which the corresponding forward problem is constrained by physical principles is challenging. This is especially true if the dimension of the inferred vector is large and the prior information about it is in the form of a collection of samples. In this work, a novel deep learning based approach is developed and applied to solving these types of problems. The approach utilizes samples of the inferred vector drawn from the prior distribution and a physics-based forward model to generate training data for a conditional Wasserstein generative adversarial network (cWGAN). The cWGAN learns the probability distribution for the inferred vector conditioned on the measurement and produces samples from this distribution. The cWGAN developed in this work differs from earlier versions in that its critic is required to be 1-Lipschitz with respect to both the inferred and the measurement vectors and not just the former. This leads to a loss term with the full (and not partial) gradient penalty. It is shown that this rather simple change leads to a stronger notion of convergence for the conditional density learned by the cWGAN and a more robust and accurate sampling strategy. Through numerical examples it is shown that this change also translates to better accuracy when solving inverse problems. The numerical examples considered include illustrative problems where the true distribution and/or statistics are known, and a more complex inverse problem motivated by applications in biomechanics.

Recent sparse MRI reconstruction models have used Deep Neural Networks (DNNs) to reconstruct relatively high-quality images from highly undersampled k-space data, enabling much faster MRI scanning. However, these techniques sometimes struggle to reconstruct sharp images that preserve fine detail while maintaining a natural appearance. In this work, we enhance the image quality by using a Conditional Wasserstein Generative Adversarial Network combined with a novel Adaptive Gradient Balancing technique that stabilizes the training and minimizes the degree of artifacts, while maintaining a high-quality reconstruction that produces sharper images than other techniques.

Topology design optimization offers a tremendous opportunity in design and manufacturing freedoms by designing and producing a part from the ground-up without a meaningful initial design as required by conventional shape design optimization approaches. Ideally, with adequate problem statements, to formulate and solve the topology design problem using a standard topology optimization process, such as SIMP (Simplified Isotropic Material with Penalization) is possible. However, in reality, an estimated over thousands of design iterations is often required for just a few design variables, the conventional optimization approach is, in general, impractical or computationally unachievable for real-world applications significantly diluting the development of the topology optimization technology. There is, therefore, a need for a different approach that will be able to optimize the initial design topology effectively and rapidly. In this study, a novel topology optimization approach based on conditional Wasserstein generative adversarial networks (CWGAN) is developed to replicate the conventional topology optimization algorithms in an extremely computationally inexpensive way. CWGAN consists of a generator and a discriminator, both of which are deep convolutional neural networks (CNN). The limited samples of data, quasi-optimal planar structures, needed for training purposes are generated using the conventional topology optimization algorithms. With CWGANs, the topology optimization conditions can be set to a required value before generating samples.