Teseo Schneider

Teseo Schneider, Yixin Hu, Xifeng Gao et al.

The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs. The goal of his benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance.

Teseo Schneider, Jeremie Dumas, Xifeng Gao et al.

We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order basis on its elements, combining triquadratic B-splines, triquadratic hexahedra (27 degrees of freedom), and harmonic elements. We demonstrate that our approach converges cubically under refinement, while requiring around 50% of the degrees of freedom than a similarly dense hexahedral mesh composed of triquadratic hexahedra. We validate our approach solving Poisson's equation on a large collection of models, which are automatically processed by our algorithm, only requiring the user to provide boundary conditions on their surface.

Nafiseh Izadyar, Sai Chandra Madduri, Teseo Schneider

Boundary representation (B-rep) generated from computer-aided design (CAD) is widely used in industry, with several large datasets available. However, the data in these datasets is represented in STEP format, requiring a CAD kernel to read and process it. This dramatically limits their scope and usage in large learning pipelines, as it constrains the possibility of deploying them on computing clusters due to the high cost of per-node licenses. This paper introduces an alternative format based on the open, cross-platform format HDF5 and a corresponding dataset for STEP files, paired with an open-source library to query and process them. Our Python package also provides standard functionalities such as sampling, normals, and curvature to ease integration in existing pipelines. To demonstrate the effectiveness of our format, we converted the Fusion 360 dataset and the ABC dataset. We developed four standard use cases (normal estimation, denoising, surface reconstruction, and segmentation) to assess the integrity of the data and its compliance with the original STEP files.

Nafiseh Izadyar, Teseo Schneider

Most existing 3D shape datasets and models focus solely on geometry, overlooking the material properties that determine how objects appear. We introduce a two-stage large language model (LLM) based method for inferring material composition directly from 3D point clouds with coarse segmentations. Our key insight is to decouple reasoning about what an object is from what it is made of. In the first stage, an LLM predicts the object's semantic; in the second stage, it assigns plausible materials to each geometric segment, conditioned on the inferred semantics. Both stages operate in a zero-shot manner, without task-specific training. Because existing datasets lack reliable material annotations, we evaluate our method using an LLM-as-a-Judge implemented in DeepEval. Across 1,000 shapes from Fusion/ABS and ShapeNet, our method achieves high semantic and material plausibility. These results demonstrate that language models can serve as general-purpose priors for bridging geometric reasoning and material understanding in 3D data.

Yibo Liu, Liam Shatzel, Brandon Haworth et al.

Animating and simulating crowds using an agent-based approach is a well-established area where every agent in the crowd is individually controlled such that global human-like behaviour emerges. We observe that human navigation and movement in crowds are often influenced by complex social and environmental interactions, driven mainly by language and dialogue. However, most existing work does not consider these dimensions and leads to animations where agent-agent and agent-environment interactions are largely limited to steering and fixed higher-level goal extrapolation. We propose a novel method that exploits large language models (LLMs) to control agents' movement. Our method has two main components: a dialogue system and language-driven navigation. We periodically query agent-centric LLMs conditioned on character personalities, roles, desires, and relationships to control the generation of inter-agent dialogue when necessitated by the spatial and social relationships with neighbouring agents. We then use the conversation and each agent's personality, emotional state, vision, and physical state to control the navigation and steering of each agent. Our model thus enables agents to make motion decisions based on both their perceptual inputs and the ongoing dialogue. We validate our method in two complex scenarios that exemplify the interplay between social interactions, steering, and crowding. In these scenarios, we observe that grouping and ungrouping of agents automatically occur. Additionally, our experiments show that our method serves as an information-passing mechanism within the crowd. As a result, our framework produces more realistic crowd simulations, with emergent group behaviours arising naturally from any environmental setting.

YunFan Zhou, Daniel Zint, Nafiseh Izadyar et al.

Parametric boundary representation models (B-Reps) are the de facto standard in CAD, graphics, and robotics, yet converting them into valid meshes remains fragile. The difficulty originates from the unavoidable approximation of high-order surface and curve intersections to low-order primitives: the resulting geometric realization often fails to respect the exact topology encoded in the B-Rep, producing meshes with incorrect or missing adjacencies. Existing meshing pipelines address these inconsistencies through heuristic feature-merging and repair strategies that offer no topological guarantees and frequently fail on complex models. We propose a fundamentally different approach: the B-Rep topology is treated as an invariant of the meshing process. Our algorithm enforces the exact B-Rep topology while allowing a single user-defined tolerance to control the deviation of the mesh from the underlying parametric surfaces. Consequently, for any admissible tolerance, the output mesh is topologically correct; only its geometric fidelity degrades as the tolerance increases. This decoupling eliminates the need for post-hoc repairs and yields robust meshes even when the underlying geometry is inconsistent or highly approximated. We evaluate our method on thousands of real-world CAD models from the ABC and Fusion 360 repositories, including instances that fail with standard meshing tools. The results demonstrate that topological guarantees at the algorithmic level enable reliable mesh generation suitable for downstream applications.

Yibo Liu, Zhixin Fang, Sune Darkner et al.

We propose mesh-free fluid simulations that exploit a kinematic neural basis for velocity fields represented by an MLP. We design a set of losses that ensures that these neural bases approximate fundamental physical properties such as orthogonality, divergence-free, boundary alignment, and smoothness. Our neural bases can then be used to fit an input sketch of a flow, which will inherit the same fundamental properties from the bases. We then can animate such flow in real-time using standard time integrators. Our neural bases can accommodate different domains, moving boundaries, and naturally extend to three dimensions.

Karl Otness, Arvi Gjoka, Joan Bruna et al.

Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations methods, motivated by the opportunity to reduce computational costs and/or learn new physical models leveraging access to large collections of data. However, the diversity of problem settings and applications has led to a plethora of approaches, each one evaluated on a different setup and with different evaluation metrics. We introduce a set of benchmark problems to take a step towards unified benchmarks and evaluation protocols. We propose four representative physical systems, as well as a collection of both widely used classical time integrators and representative data-driven methods (kernel-based, MLP, CNN, nearest neighbors). Our framework allows evaluating objectively and systematically the stability, accuracy, and computational efficiency of data-driven methods. Additionally, it is configurable to permit adjustments for accommodating other learning tasks and for establishing a foundation for future developments in machine learning for scientific computing.

Ruiqi Ni, Teseo Schneider, Daniele Panozzo et al.

Generating locally optimal UAV-trajectories is challenging due to the non-convex constraints of collision avoidance and actuation limits. We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees the validity and asymptotic optimality for known environments. \textit{Validity:} Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization. \textit{Asymptotic Optimality:} We use an asymptotic exact piecewise approximation of the trajectory with an automatically adjustable resolution of its discretization. The trajectory converges under refinement to the first-order stationary point of the exact non-convex programming problem. Our method has additional practical advantages including joint optimality in terms of trajectory and time-allocation, and robustness to challenging environments as demonstrated in our experiments.

Francis Williams, Teseo Schneider, Claudio Silva et al.

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for surface reconstruction. Specifically, we overfit a neural network representing a local chart parameterization to part of an input point cloud using the Wasserstein distance as a measure of approximation. By jointly fitting many such networks to overlapping parts of the point cloud, while enforcing a consistency condition, we compute a manifold atlas. By sampling this atlas, we can produce a dense reconstruction of the surface approximating the input cloud. The entire procedure does not require any training data or explicit regularization, yet, we show that it is able to perform remarkably well: not introducing typical overfitting artifacts, and approximating sharp features closely at the same time. We experimentally show that this geometric prior produces good results for both man-made objects containing sharp features and smoother organic objects, as well as noisy inputs. We compare our method with a number of well-known reconstruction methods on a standard surface reconstruction benchmark.