Forward Gradients for Data-Driven CFD Wall Modeling

Computational Fluid Dynamics (CFD) is used in the design and optimization of gas turbines and many other industrial/ scientific applications. However, the practical use is often limited by the high computational cost, and the accurate resolution of near-wall flow is a significant contributor to this cost. Machine learning (ML) and other data-driven methods can complement existing wall models. Nevertheless, training these models is bottlenecked by the large computational effort and memory footprint demanded by back-propagation. Recent work has presented alternatives for computing gradients of neural networks where a separate forward and backward sweep is not needed and storage of intermediate results between sweeps is not required because an unbiased estimator for the gradient is computed in a single forward sweep. In this paper, we discuss the application of this approach for training a subgrid wall model that could potentially be used as a surrogate in wall-bounded flow CFD simulations to reduce the computational overhead while preserving predictive accuracy.

Self-supervised Learning for Anomaly Detection in Computational Workflows

Anomaly detection is the task of identifying abnormal behavior of a system. Anomaly detection in computational workflows is of special interest because of its wide implications in various domains such as cybersecurity, finance, and social networks. However, anomaly detection in computational workflows~(often modeled as graphs) is a relatively unexplored problem and poses distinct challenges. For instance, when anomaly detection is performed on graph data, the complex interdependency of nodes and edges, the heterogeneity of node attributes, and edge types must be accounted for. Although the use of graph neural networks can help capture complex inter-dependencies, the scarcity of labeled anomalous examples from workflow executions is still a significant challenge. To address this problem, we introduce an autoencoder-driven self-supervised learning~(SSL) approach that learns a summary statistic from unlabeled workflow data and estimates the normal behavior of the computational workflow in the latent space. In this approach, we combine generative and contrastive learning objectives to detect outliers in the summary statistics. We demonstrate that by estimating the distribution of normal behavior in the latent space, we can outperform state-of-the-art anomaly detection methods on our benchmark datasets.

Learning Continually on a Sequence of Graphs -- The Dynamical System Way

Continual learning~(CL) is a field concerned with learning a series of inter-related task with the tasks typically defined in the sense of either regression or classification. In recent years, CL has been studied extensively when these tasks are defined using Euclidean data-- data, such as images, that can be described by a set of vectors in an n-dimensional real space. However, the literature is quite sparse, when the data corresponding to a CL task is nonEuclidean-- data , such as graphs, point clouds or manifold, where the notion of similarity in the sense of Euclidean metric does not hold. For instance, a graph is described by a tuple of vertices and edges and similarities between two graphs is not well defined through a Euclidean metric. Due to this fundamental nature of the data, developing CL for nonEuclidean data presents several theoretical and methodological challenges. In particular, CL for graphs requires explicit modelling of nonstationary behavior of vertices and edges and their effects on the learning problem. Therefore, in this work, we develop a adaptive dynamic programming viewpoint for CL with graphs. In this work, we formulate a two-player sequential game between the act of learning new tasks~(generalization) and remembering previously learned tasks~(forgetting). We prove mathematically the existence of a solution to the game and demonstrate convergence to the solution of the game. Finally, we demonstrate the efficacy of our method on a number of graph benchmarks with a comprehensive ablation study while establishing state-of-the-art performance.

Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles

Classical problems in computational physics such as data-driven forecasting and signal reconstruction from sparse sensors have recently seen an explosion in deep neural network (DNN) based algorithmic approaches. However, most DNN models do not provide uncertainty estimates, which are crucial for establishing the trustworthiness of these techniques in downstream decision making tasks and scenarios. In recent years, ensemble-based methods have achieved significant success for the uncertainty quantification in DNNs on a number of benchmark problems. However, their performance on real-world applications remains under-explored. In this work, we present an automated approach to DNN discovery and demonstrate how this may also be utilized for ensemble-based uncertainty quantification. Specifically, we propose the use of a scalable neural and hyperparameter architecture search for discovering an ensemble of DNN models for complex dynamical systems. We highlight how the proposed method not only discovers high-performing neural network ensembles for our tasks, but also quantifies uncertainty seamlessly. This is achieved by using genetic algorithms and Bayesian optimization for sampling the search space of neural network architectures and hyperparameters. Subsequently, a model selection approach is used to identify candidate models for an ensemble set construction. Afterwards, a variance decomposition approach is used to estimate the uncertainty of the predictions from the ensemble. We demonstrate the feasibility of this framework for two tasks - forecasting from historical data and flow reconstruction from sparse sensors for the sea-surface temperature. We demonstrate superior performance from the ensemble in contrast with individual high-performing models and other benchmarks.

Cooperative Deep $Q$-learning Framework for Environments Providing Image Feedback

In this paper, we address two key challenges in deep reinforcement learning setting, sample inefficiency and slow learning, with a dual NN-driven learning approach. In the proposed approach, we use two deep NNs with independent initialization to robustly approximate the action-value function in the presence of image inputs. In particular, we develop a temporal difference (TD) error-driven learning approach, where we introduce a set of linear transformations of the TD error to directly update the parameters of each layer in the deep NN. We demonstrate theoretically that the cost minimized by the error-driven learning (EDL) regime is an approximation of the empirical cost and the approximation error reduces as learning progresses, irrespective of the size of the network. Using simulation analysis, we show that the proposed methods enables faster learning and convergence and requires reduced buffer size (thereby increasing the sample efficiency).

Learning to Control using Image Feedback

Learning to control complex systems using non-traditional feedback, e.g., in the form of snapshot images, is an important task encountered in diverse domains such as robotics, neuroscience, and biology (cellular systems). In this paper, we present a two neural-network (NN)-based feedback control framework to design control policies for systems that generate feedback in the form of images. In particular, we develop a deep $Q$-network (DQN)-driven learning control strategy to synthesize a sequence of control inputs from snapshot images that encode the information pertaining to the current state and control action of the system. Further, to train the networks we employ a direct error-driven learning (EDL) approach that utilizes a set of linear transformations of the NN training error to update the NN weights in each layer. We verify the efficacy of the proposed control strategy using numerical examples.

AutoDEUQ: Automated Deep Ensemble with Uncertainty Quantification

Deep neural networks are powerful predictors for a variety of tasks. However, they do not capture uncertainty directly. Using neural network ensembles to quantify uncertainty is competitive with approaches based on Bayesian neural networks while benefiting from better computational scalability. However, building ensembles of neural networks is a challenging task because, in addition to choosing the right neural architecture or hyperparameters for each member of the ensemble, there is an added cost of training each model. We propose AutoDEUQ, an automated approach for generating an ensemble of deep neural networks. Our approach leverages joint neural architecture and hyperparameter search to generate ensembles. We use the law of total variance to decompose the predictive variance of deep ensembles into aleatoric (data) and epistemic (model) uncertainties. We show that AutoDEUQ outperforms probabilistic backpropagation, Monte Carlo dropout, deep ensemble, distribution-free ensembles, and hyper ensemble methods on a number of regression benchmarks.

Formalizing the Generalization-Forgetting Trade-off in Continual Learning

We formulate the continual learning (CL) problem via dynamic programming and model the trade-off between catastrophic forgetting and generalization as a two-player sequential game. In this approach, player 1 maximizes the cost due to lack of generalization whereas player 2 minimizes the cost due to catastrophic forgetting. We show theoretically that a balance point between the two players exists for each task and that this point is stable (once the balance is achieved, the two players stay at the balance point). Next, we introduce balanced continual learning (BCL), which is designed to attain balance between generalization and forgetting and empirically demonstrate that BCL is comparable to or better than the state of the art.