Neural Information Processing Systems http://nips.cc/

Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction.

Active subspace analysis uses the leading eigenspace of the gradient's second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator which coincides with the active subspace matrix when applied to a Euclidean space. We show that many of the desirable properties of Active Subspace analysis extend directly to the infinite dimensional setting. We also propose a Monte Carlo procedure and discuss its convergence properties. Finally, we deploy this methodology to create visualizations and improve modeling and optimization on complex test problems.

Neural Information Processing Systems http://nips.cc/

Bayesian optimization (BO ) is an effective method for optimizing expensive-to-evaluate black-box functions. While high-dimensional problems can be particularly challenging, due to the multitude of parameter choices and the potentially high number of data points required to fit the model, this limitation can be addressed if the problem satisfies simplifying assumptions. Axis-aligned subspace approaches, where few dimensions have a significant impact on the objective, motivated several algorithms for high-dimensional BO . However, the validity of this assumption is rarely verified, and the assumption is rarely exploited to its full extent. We propose a group testing ( GT) approach to identify active variables to facilitate efficient optimization in these domains. The proposed algorithm, Group Testing Bayesian Optimization (GTBO), first runs a testing phase where groups of variables are systematically selected and tested on whether they influence the objective, then terminates once active dimensions are identified. To that end, we extend the well-established GT theory to functions over continuous domains. In the second phase, GTBO guides optimization by placing more importance on the active dimensions. By leveraging the axis-aligned subspace assumption, GTBO outperforms state-of-the-art methods on benchmarks satisfying the assumption of axis-aligned subspaces, while offering improved interpretability.

We propose nonuniform data-driven parameter distributions for neural network initialization based on derivative data of the function to be approximated. These parameter distributions are developed in the context of non-parametric regression models based on shallow neural networks, and compare favorably to well-established uniform random feature models based on conventional weight initialization. We address the cases of Heaviside and ReLU activation functions, and their smooth approximations (sigmoid and softplus), and use recent results on the harmonic analysis and sparse representation of neural networks resulting from fully trained optimal networks. Extending analytic results that give exact representation, we obtain densities that concentrate in regions of the parameter space corresponding to neurons that are well suited to model the local derivatives of the unknown function. Based on these results, we suggest simplifications of these exact densities based on approximate derivative data in the input points that allow for very efficient sampling and lead to performance of random feature models close to optimal networks in several scenarios.

In recent years, deep generative models have been successfully adopted for various molecular design tasks, particularly in the life and material sciences. A critical challenge for pre-trained generative molecular design (GMD) models is to fine-tune them to be better suited for downstream design tasks aimed at optimizing specific molecular properties. However, redesigning and training an existing effective generative model from scratch for each new design task is impractical. Furthermore, the black-box nature of typical downstream tasks$\unicode{x2013}$such as property prediction$\unicode{x2013}$makes it nontrivial to optimize the generative model in a task-specific manner. In this work, we propose a novel approach for a model uncertainty-guided fine-tuning of a pre-trained variational autoencoder (VAE)-based GMD model through performance feedback in an active learning setting. The main idea is to quantify model uncertainty in the generative model, which is made efficient by working within a low-dimensional active subspace of the high-dimensional VAE parameters explaining most of the variability in the model's output. The inclusion of model uncertainty expands the space of viable molecules through decoder diversity. We then explore the resulting model uncertainty class via black-box optimization made tractable by low-dimensionality of the active subspace. This enables us to identify and leverage a diverse set of high-performing models to generate enhanced molecules. Empirical results across six target molecular properties, using multiple VAE-based generative models, demonstrate that our uncertainty-guided fine-tuning approach consistently outperforms the original pre-trained models.

Regression trees have emerged as a preeminent tool for solving real-world regression problems due to their ability to deal with nonlinearities, interaction effects and sharp discontinuities. In this article, we rather study regression trees applied to well-behaved, differentiable functions, and determine the relationship between node parameters and the local gradient of the function being approximated. We find a simple estimate of the gradient which can be efficiently computed using quantities exposed by popular tree learning libraries. This allows the tools developed in the context of differentiable algorithms, like neural nets and Gaussian processes, to be deployed to tree-based models. To demonstrate this, we study measures of model sensitivity defined in terms of integrals of gradients and demonstrate how to compute them for regression trees using the proposed gradient estimates. Quantitative and qualitative numerical experiments reveal the capability of gradients estimated by regression trees to improve predictive analysis, solve tasks in uncertainty quantification, and provide interpretation of model behavior.

Deep generative models have been accelerating the inverse design process in material and drug design. Unlike their counterpart property predictors in typical molecular design frameworks, generative molecular design models have seen fewer efforts on uncertainty quantification (UQ) due to computational challenges in Bayesian inference posed by their large number of parameters. In this work, we focus on the junction-tree variational autoencoder (JT-VAE), a popular model for generative molecular design, and address this issue by leveraging the low dimensional active subspace to capture the uncertainty in the model parameters. Specifically, we approximate the posterior distribution over the active subspace parameters to estimate the epistemic model uncertainty in an extremely high dimensional parameter space. The proposed UQ scheme does not require alteration of the model architecture, making it readily applicable to any pre-trained model. Our experiments demonstrate the efficacy of the AS-based UQ and its potential impact on molecular optimization by exploring the model diversity under epistemic uncertainty.

In the early stages of aerospace design, reduced order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy of aerospace design demands the use of high-dimensional design spaces to capture detailed features and design variability accurately. However, these spaces introduce significant challenges, including the curse of dimensionality, which stems from both high-dimensional inputs and outputs necessitating substantial training data and computational effort. To address these complexities, this study introduces a novel multi-fidelity, parametric, and non-intrusive ROM framework designed for high-dimensional contexts. It integrates machine learning techniques for manifold alignment and dimension reduction employing Proper Orthogonal Decomposition (POD) and Model-based Active Subspace with multi-fidelity regression for ROM construction. Our approach is validated through two test cases: the 2D RAE~2822 airfoil and the 3D NASA CRM wing, assessing combinations of various fidelity levels, training data ratios, and sample sizes. Compared to the single-fidelity PCAS method, our multi-fidelity solution offers improved cost-accuracy benefits and achieves better predictive accuracy with reduced computational demands. Moreover, our methodology outperforms the manifold-aligned ROM (MA-ROM) method by 50% in handling scenarios with large input dimensions, underscoring its efficacy in addressing the complex challenges of aerospace design.