Denoising is an important post-processing step in physically based Monte Carlo (MC) rendering. While neural networks are widely used in practice, statistical analysis has recently become a viable alternative for denoising. In this paper, we present a general framework for statistics-based error reduction of both estimated radiance and variance. Specifically, we introduce a novel denoising approach for variance estimates, which can either improve variance-aware adaptive sampling or provide additional input for image denoising in a cascaded manner. Furthermore, we present multi-transform denoising: a general and efficient correction scheme for non-normal distributions, which typically occur in MC rendering. All these contributions combine to a robust denoising pipeline that does not require any pretraining and can run efficiently on current GPU hardware. Our results show distinct advantages over previous denoising methods, especially in the range of a few hundred samples per pixel, which is of high practical relevance. Finally, we demonstrate good convergence behavior as the number of samples increases, providing predictable results with low bias that are free of hallucinated neural artifacts. In summary, our statistics-based algorithms for adaptive sampling and denoising deliver fast, consistent, low-bias variance and radiance estimates.

Abstract The early phase of urban planning and architectural design has a great impact on the thermal loads and characteristics of constructed buildings. It is, therefore, important to efficiently simulate thermal effects early on and rectify possible problems. In this paper, we present an inverse simulation of radiative heat transport and a differentiable photon‐tracing approach. Our method utilizes GPU‐accelerated ray tracing to speed up both the forward and adjoint simulation. Moreover, we incorporate matrix compression to further increase the efficiency of our thermal solver and support larger scenes. In addition to our differentiable photon‐tracing approach, we introduce a novel approximate edge sampling scheme that re‐uses primary samples instead of relying on explicit edge samples or auxiliary rays to resolve visibility discontinuities. Our inverse simulation system enables designers to not only predict the temperature distribution, but also automatically optimize the design to improve thermal comfort and avoid problematic configurations. We showcase our approach using several examples in which we optimize the placement of buildings or their facade geometry. Our approach can be used to optimize arbitrary geometric parameterizations and supports steady‐state, as well as transient simulations.

Differentiable rendering methods promise the ability to optimize various parameters of three-dimensional (3D) scenes to achieve a desired result. However, lighting design has so far received little attention in this field. In this article, we introduce a method that enables continuous optimization of the arrangement of luminaires in a 3D scene via differentiable light tracing. Our experiments show two major issues when attempting to apply existing methods from differentiable path tracing to this problem: First, many rendering methods produce images, which restricts the ability of a designer to define lighting objectives to image space. Second, most previous methods are designed for scene geometry or material optimization and have not been extensively tested for the case of optimizing light sources. Currently available differentiable ray-tracing methods do not provide satisfactory performance, even on fairly basic test cases in our experience. In this article, we propose, to the best of our knowledge, a novel adjoint light tracing method that overcomes these challenges and enables gradient-based lighting design optimization in a view-independent (camera-free) way. Thus, we allow the user to paint illumination targets directly onto the 3D scene or use existing baked illumination data (e.g., light maps). Using modern ray-tracing hardware, we achieve interactive performance. We find light tracing advantageous over path tracing in this setting, as it naturally handles irregular geometry, resulting in less noise and improved optimization convergence. We compare our adjoint gradients to state-of-the-art image-based differentiable rendering methods. We also demonstrate that our gradient data works with various common optimization algorithms, providing good convergence behaviour. Qualitative comparisons with real-world scenes underline the practical applicability of our method.

Architectural design and urban planning are complex design tasks. Predicting the thermal impact of design choices at interactive rates enhances the ability of designers to improve energy efficiency and avoid problematic heat islands while maintaining design quality. We show how to use and adapt methods from computer graphics to efficiently simulate heat transfer via thermal radiation, thereby improving user guidance in the early design phase of large-scale construction projects and helping to increase energy efficiency and outdoor comfort. Our method combines a hardware-accelerated photon tracing approach with a carefully selected finite element discretization, inspired by precomputed radiance transfer. This combination allows us to precompute a radiative transport operator, which we then use to rapidly solve either steady-state or transient heat transport throughout the entire scene. Our formulation integrates time-dependent solar irradiation data without requiring changes in the transport operator, allowing us to quickly analyze many different scenarios such as common weather patterns, monthly or yearly averages, or transient simulations spanning multiple days or weeks. We show how our approach can be used for interactive design workflows such as city planning via fast feedback in the early design phase.

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.

This paper presents a method for optimizing visco-elastic material parameters of a finite element simulation to best approximate the dynamic motion of real-world soft objects. We compute the gradient with respect to the material parameters of a least-squares error objective function using either direct sensitivity analysis or an adjoint state method. We then optimize the material parameters such that the simulated motion matches real-world observations as closely as possible. In this way, we can directly build a useful simulation model that captures the visco-elastic behaviour of the specimen of interest. We demonstrate the effectiveness of our method on various examples such as numerical coarsening, custom-designed objective functions, and of course real-world flexible elastic objects made of foam or 3D printed lattice structures, including a demo application in soft robotics.

Databases are one of the great success stories in IT. However, they have been continuously increasing in complexity, hampering operation, maintenance, and upgrades. To face this complexity, sophisticated methods for schema summarization, data cleaning, information integration, and many more have been devised that usually rely on data profiles, such as data statistics, signatures, and integrity constraints. Such data profiles are often extracted by automatic algorithms, which entails various problems: The profiles can be unfiltered and huge in volume; different profile types require different complex data structures; and the various profile types are not integrated with each other. We introduce Metacrate, a system to store, organize, and analyze data profiles of relational databases, thereby following the proven design of databases. In particular, we (i) propose a logical and a physical data model to store all kinds of data profiles in a scalable fashion; (ii) describe an analytics layer to query, integrate, and analyze the profiles efficiently; and (iii) implement on top a library of established algorithms to serve use cases, such as schema discovery, database refactoring, and data cleaning.

We propose a novel surface-only technique for simulating incompressible, inviscid and uniform-density liquids with surface tension in three dimensions. The liquid surface is captured by a triangle mesh on which a Lagrangian velocity field is stored. Because advection of the velocity field may violate the incompressibility condition, we devise an orthogonal projection technique to remove the divergence while requiring the evaluation of only two boundary integrals. The forces of surface tension, gravity, and solid contact are all treated by a boundary element solve, allowing us to perform detailed simulations of a wide range of liquid phenomena, including waterbells, droplet and jet collisions, fluid chains, and crown splashes.

We present a boundary element based method for fast simulation of brittle fracture. By introducing simplifying assumptions that allow us to quickly estimate stress intensities and opening displacements during crack propagation, we build a fracture algorithm where the cost of each time step scales linearly with the length of the crack-front. The transition from a full boundary element method to our faster variant is possible at the beginning of any time step. This allows us to build a hybrid method, which uses the expensive but more accurate BEM while the number of degrees of freedom is low, and uses the fast method once that number exceeds a given threshold as the crack geometry becomes more complicated. Furthermore, we integrate this fracture simulation with a standard rigid-body solver. Our rigid-body coupling solves a Neumann boundary value problem by carefully separating translational, rotational and deformational components of the collision forces and then applying a Tikhonov regularizer to the resulting linear system. We show that our method produces physically reasonable results in standard test cases and is capable of dealing with complex scenes faster than previous finite- or boundary element approaches.

We present a method for simulating brittle fracture under the assumptions of quasi-static linear elastic fracture mechanics (LEFM). Using the boundary element method (BEM) and Lagrangian crack-fronts, we produce highly detailed fracture surfaces. The computational cost of the BEM is alleviated by using a low-resolution mesh and interpolating the resulting stress intensity factors when propagating the high-resolution crack-front. Our system produces physics-based fracture surfaces with high spatial and temporal resolution, taking spatial variation of material toughness and/or strength into account. It also allows for crack initiation to be handled separately from crack propagation, which is not only more reasonable from a physics perspective, but can also be used to control the simulation. Separating the resolution of the crack-front from the resolution of the computational mesh increases the efficiency and therefore the amount of visual detail on the resulting fracture surfaces. The BEM also allows us to re-use previously computed blocks of the system matrix.

Decentralized partially observable Markov decision processes (Dec-POMDPs) model cooperative multiagent scenarios, providing a powerful general framework for team-based artificial intelligence. While optimal algorithms exist for Dec-POMDPs, theoretical and empirical results demonstrate that they are impractical for many problems of real interest. We examine the use of reinforcement learning (RL) as a means to generate adequate, if not optimal, joint policies for Dec-POMDPs. It is easily demonstrated (and expected) that single-agent RL produces results of little joint utility. We therefore investigate heuristic methods, based upon the dynamics of the Dec-POMDP formulation, that bias the learning process to produce coordinated action. Empirical tests on a benchmark problem show that these heuristics significantly enhance learning performance, even out-performing a hand-crafted heuristic in cases where the learning process converges quickly.