Renato Pajarola

Rafael Ballester-Ripoll, Enrique G. Paredes, Renato Pajarola

Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (TT) as a unified framework for surrogate modeling and global sensitivity analysis via Sobol indices. We first overview several strategies to build a TT surrogate of the unknown true model using either an adaptive sampling strategy or a predefined set of samples. We then introduce and derive the Sobol tensor train, which compactly represents the Sobol indices for all possible joint variable interactions which are infeasible to compute and store explicitly. Our formulation allows efficient aggregation and subselection operations: we are able to obtain related indices (closed, total, and superset indices) at negligible cost. Furthermore, we exploit an existing global optimization procedure within the TT framework for variable selection and model analysis tasks. We demonstrate our algorithms with two analytical engineering models and a parallel computing simulation data set.

Rafael Ballester-Ripoll, Enrique G. Paredes, Renato Pajarola

Following up on the success of the analysis of variance (ANOVA) decomposition and the Sobol indices (SI) for global sensitivity analysis, various related quantities of interest have been defined in the literature including the effective and mean dimensions, the dimension distribution, and the Shapley values. Such metrics combine up to exponential numbers of SI in different ways and can be of great aid in uncertainty quantification and model interpretation tasks, but are computationally challenging. We focus on surrogate based sensitivity analysis for independently distributed variables, namely via the tensor train (TT) decomposition. This format permits flexible and scalable surrogate modeling and can efficiently extract all SI at once in a compressed TT representation of their own. Based on this, we contribute a range of novel algorithms that compute more advanced sensitivity metrics by selecting and aggregating certain subsets of SI in the tensor compressed domain. Drawing on an interpretation of the TT model in terms of deterministic finite automata, we are able to construct explicit auxiliary TT tensors that encode exactly all necessary index selection masks. Having both the SI and the masks in the TT format allows efficient computation of all aforementioned metrics, as we demonstrate in a number of example models.

Philipp Erler, Lizeth Fuentes, Pedro Hermosilla et al.

3D surface reconstruction from point clouds is a key step in areas such as content creation, archaeology, digital cultural heritage, and engineering. Current approaches either try to optimize a non-data-driven surface representation to fit the points, or learn a data-driven prior over the distribution of commonly occurring surfaces and how they correlate with potentially noisy point clouds. Data-driven methods enable robust handling of noise and typically either focus on a global or a local prior, which trade-off between robustness to noise on the global end and surface detail preservation on the local end. We propose PPSurf as a method that combines a global prior based on point convolutions and a local prior based on processing local point cloud patches. We show that this approach is robust to noise while recovering surface details more accurately than the current state-of-the-art. Our source code, pre-trained model and dataset are available at: https://github.com/cg-tuwien/ppsurf

Claudio Mura, Renato Pajarola, Konrad Schindler et al.

Recent years have seen a proliferation of new digital products for the efficient management of indoor spaces, with important applications like emergency management, virtual property showcasing and interior design. These products rely on accurate 3D models of the environments considered, including information on both architectural and non-permanent elements. These models must be created from measured data such as RGB-D images or 3D point clouds, whose capture and consolidation involves lengthy data workflows. This strongly limits the rate at which 3D models can be produced, preventing the adoption of many digital services for indoor space management. We provide an alternative to such data-intensive procedures by presenting Walk2Map, a data-driven approach to generate floor plans only from trajectories of a person walking inside the rooms. Thanks to recent advances in data-driven inertial odometry, such minimalistic input data can be acquired from the IMU readings of consumer-level smartphones, which allows for an effortless and scalable mapping of real-world indoor spaces. Our work is based on learning the latent relation between an indoor walk trajectory and the information represented in a floor plan: interior space footprint, portals, and furniture. We distinguish between recovering area-related (interior footprint, furniture) and wall-related (doors) information and use two different neural architectures for the two tasks: an image-based Encoder-Decoder and a Graph Convolutional Network, respectively. We train our networks using scanned 3D indoor models and apply them in a cascaded fashion on an indoor walk trajectory at inference time. We perform a qualitative and quantitative evaluation using both simulated and measured, real-world trajectories, and compare against a baseline method for image-to-image translation. The experiments confirm the feasibility of our approach.

Rafael Ballester-Ripoll, Renato Pajarola

Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many fields in computational science and engineering. We propose a principal component-based approach to visualize such fields that accurately reflects their sensitivity to input parameters. The method performs dimensionality reduction on the vast $L^2$ Hilbert space formed by all possible partial functions (i.e., those defined by fixing one or more input parameters to specific values), which are projected to low-dimensional parameterized manifolds such as 3D curves, surfaces, and ensembles thereof. Our mapping provides a direct geometrical and visual interpretation in terms of Sobol's celebrated method for variance-based sensitivity analysis. We furthermore contribute a practical realization of the proposed method by means of tensor decomposition, which enables accurate yet interactive integration and multilinear principal component analysis of high-dimensional models.