An Inverse Procedural Modeling Pipeline for SVBRDF Maps

Procedural modeling is now the de facto standard of material modeling in industry. Procedural models can be edited and are easily extended, unlike pixel-based representations of captured materials. In this article, we present a semi-automatic pipeline for general material proceduralization. Given Spatially Varying Bidirectional Reflectance Distribution Functions (SVBRDFs) represented as sets of pixel maps, our pipeline decomposes them into a tree of sub-materials whose spatial distributions are encoded by their associated mask maps. This semi-automatic decomposition of material maps progresses hierarchically, driven by our new spectrum-aware material matting and instance-based decomposition methods. Each decomposed sub-material is proceduralized by a novel multi-layer noise model to capture local variations at different scales. Spatial distributions of these sub-materials are modeled either by a by-example inverse synthesis method recovering Point Process Texture Basis Functions (PPTBF) [ 30 ] or via random sampling. To reconstruct procedural material maps, we propose a differentiable rendering-based optimization that recomposes all generated procedures together to maximize the similarity between our procedural models and the input material pixel maps. We evaluate our pipeline on a variety of synthetic and real materials. We demonstrate our method’s capacity to process a wide range of material types, eliminating the need for artist designed material graphs required in previous work [ 38 , 53 ]. As fully procedural models, our results expand to arbitrary resolution and enable high-level user control of appearance.

Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases

Strain energy decomposition methods in phase field fracture models separate strain energy that contributes to fracture from that which does not. However, various decomposition methods have been proposed in the literature, and it can be difficult to determine an appropriate method for a given problem. The goal of this work is to facilitate the choice of strain decomposition method by assessing the performance of three existing methods (spectral decomposition of the stress or the strain and deviatoric decomposition of the strain) and one new method (deviatoric decomposition of the stress) with several benchmark problems. In each benchmark problem, we compare the performance of the four methods using both qualitative and quantitative metrics. In the first benchmark, we compare the predicted mechanical behavior of cracked material. We then use four quasi-static benchmark cases: a single edge notched tension test, a single edge notched shear test, a three-point bending test, and a L-shaped panel test. Finally, we use two dynamic benchmark cases: a dynamic tensile fracture test and a dynamic shear fracture test. All four methods perform well in tension, the two spectral methods perform better in compression and with mixed mode (though the stress spectral method performs the best), and all the methods show minor issues in at least one of the shear cases. In general, whether the strain or the stress is decomposed does not have a significant impact on the predicted behavior.

oCEM: Automatic detection and analysis of overlapping co-expressed gene modules

Background When it comes to the co-expressed gene module detection, its typical challenges consist of overlap between identified modules and local co-expression in a subset of biological samples. The nature of module detection is the use of unsupervised clustering approaches and algorithms. Those methods are advanced undoubtedly, but the selection of a certain clustering method for sample- and gene-clustering tasks is separate, in which the latter task is often more complicated. Results This study presented an R-package, Overlapping CoExpressed gene Module (oCEM), armed with the decomposition methods to solve the challenges above. We also developed a novel auxiliary statistical approach to select the optimal number of principal components using a permutation procedure. We showed that oCEM outperformed state-of-the-art techniques in the ability to detect biologically relevant modules additionally. Conclusions oCEM helped non-technical users easily perform complicated statistical analyses and then gain robust results. oCEM and its applications, along with example data, were freely provided at https://github.com/huynguyen250896/oCEM.

Biological regulatory networks are less nonlinear than expected by chance

Nonlinearity is a characteristic of complex biological regulatory networks that has implications ranging from therapy to control. To better understand its nature, we analyzed a suite of published Boolean network models, containing a variety of complex nonlinear interactions, with an approach involving a probabilistic generalization of Boolean logic that George Boole himself had proposed. Leveraging the continuous-nature of this formulation using Taylor-decomposition methods revealed the distinct layers of nonlinearity of the models. A comparison of the resulting series of model approximations with the corresponding sets of randomized ensembles furthermore revealed that the biological networks are relatively more linearly approximable. We hypothesize that this is a result of optimization by natural selection for the purpose of controllability.

STR: Seasonal-Trend Decomposition Using Regression

We propose a new method for decomposing seasonal data: a seasonal-trend decomposition using regression (STR). Unlike other decomposition methods, STR allows for multiple seasonal and cyclic components, covariates, seasonal patterns that may have noninteger periods, and seasonality with complex topology. It can be used for time series with any regular time index, including hourly, daily, weekly, monthly, or quarterly data. It is competitive with existing methods when they exist and tackles many more decomposition problems than other methods allow. STR is based on a regularized optimization and so is somewhat related to ridge regression. Because it is based on a statistical model, we can easily compute confidence intervals for components, something that is not possible with most existing decomposition methods (such as seasonal-trend decomposition using Loess, X-12-ARIMA, SEATS-TRAMO, etc.). Our model is implemented in the R package stR, so it can be applied by anyone to their own data.

Information Extraction from Satellite-Based Polarimetric SAR Data Using Simulated Annealing and SIRT Methods and GPU Processing

The main goal of this research was to propose a new method of polarimetric SAR data decomposition that will extract additional polarimetric information from the Synthetic Aperture Radar (SAR) images compared to other existing decomposition methods. Most of the current decomposition methods are based on scattering, covariance or coherence matrices describing the radar wave-scattering phenomenon represented in a single pixel of an SAR image. A lot of different decomposition methods have been proposed up to now, but the problem is still open since it has no unique solution. In this research, a new polarimetric decomposition method is proposed that is based on polarimetric signature matrices. Such matrices may be used to reveal hidden information about the image target. Since polarimetric signatures (size 18 × 9) are much larger than scattering (size 2 × 2), covariance (size 3 × 3 or 4 × 4) or coherence (size 3 × 3 or 4 × 4) matrices, it was essential to use appropriate computational tools to calculate the results of the proposed decomposition method within an acceptable time frame. In order to estimate the effectiveness of the presented method, the obtained results were compared with the outcomes of another method of decomposition (Arii decomposition). The conducted research showed that the proposed solution, compared with Arii decomposition, does not overestimate the volume-scattering component in built-up areas and clearly separates objects within the mixed-up areas, where both building, vegetation and surfaces occur.

Mixed-Projection Conic Optimization: A New Paradigm for Modeling Rank Constraints

Many central problems throughout optimization, machine learning, and statistics are equivalent to optimizing a low-rank matrix over a convex set. However, although rank constraints offer unparalleled modeling flexibility, no generic code currently solves these problems to certifiable optimality at even moderate sizes. Instead, low-rank optimization problems are solved via convex relaxations or heuristics that do not enjoy optimality guarantees. In “Mixed-Projection Conic Optimization: A New Paradigm for Modeling Rank Constraints,” Bertsimas, Cory-Wright, and Pauphilet propose a new approach for modeling and optimizing over rank constraints. They generalize mixed-integer optimization by replacing binary variables z that satisfy z2 =z with orthogonal projection matrices Y that satisfy Y2 = Y. This approach offers the following contributions: First, it supplies certificates of (near) optimality for low-rank problems. Second, it demonstrates that some of the best ideas in mixed-integer optimization, such as decomposition methods, cutting planes, relaxations, and random rounding schemes, admit straightforward extensions to mixed-projection optimization.

ANALYSIS OF METHODS OF INCREASING DATA RELIABILITY FOR PROBLEMS OF SHORT TERM FORECASTING OF NODAL LOAD

A comparative analysis of clustering methods was performed to identify gaps and anomalous values in the data. Data from the northwestern region of the United States were used for evaluation. According to the analysis results, it was found that the use of the DBSCAN method leads to a much smaller number of false positives. An algorithm for two-stage data validation using clustering and time series decomposition methods is proposed. Ref.9, fig. 3, tables 3.