Physically Compatible 3D Object Modeling from a Single Image

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes

We present TetSphere splatting, an explicit, Lagrangian representation for reconstructing 3D shapes with high-quality geometry. In contrast to conventional object reconstruction methods which predominantly use Eulerian representations, including both neural implicit (e.g., NeRF, NeuS) and explicit representations (e.g., DMTet), and often struggle with high computational demands and suboptimal mesh quality, TetSphere splatting utilizes an underused but highly effective geometric primitive -- tetrahedral meshes. This approach directly yields superior mesh quality without relying on neural networks or post-processing. It deforms multiple initial tetrahedral spheres to accurately reconstruct the 3D shape through a combination of differentiable rendering and geometric energy optimization, resulting in significant computational efficiency. Serving as a robust and versatile geometry representation, Tet-Sphere splatting seamlessly integrates into diverse applications, including single-view 3D reconstruction, image-/text-to-3D content generation. Experimental results demonstrate that TetSphere splatting outperforms existing representations, delivering faster optimization speed, enhanced mesh quality, and reliable preservation of thin structures.

LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery

Large Language Models have recently gained significant attention in scientific discovery for their extensive knowledge and advanced reasoning capabilities. However, they encounter challenges in effectively simulating observational feedback and grounding it with language to propel advancements in physical scientific discovery. Conversely, human scientists undertake scientific discovery by formulating hypotheses, conducting experiments, and revising theories through observational analysis. Inspired by this, we propose to enhance the knowledge-driven, abstract reasoning abilities of LLMs with the computational strength of simulations. We introduce Scientific Generative Agent (SGA), a bilevel optimization framework: LLMs act as knowledgeable and versatile thinkers, proposing scientific hypotheses and reason about discrete components, such as physics equations or molecule structures; meanwhile, simulations function as experimental platforms, providing observational feedback and optimizing via differentiability for continuous parts, such as physical parameters. We conduct extensive experiments to demonstrate our framework's efficacy in constitutive law discovery and molecular design, unveiling novel solutions that differ from conventional human expectations yet remain coherent upon analysis.

Representing Molecules as Random Walks Over Interpretable Grammars

Recent research in molecular discovery has primarily been devoted to small, drug-like molecules, leaving many similarly important applications in material design without adequate technology. These applications often rely on more complex molecular structures with fewer examples that are carefully designed using known substructures. We propose a data-efficient and interpretable model for representing and reasoning over such molecules in terms of graph grammars that explicitly describe the hierarchical design space featuring motifs to be the design basis. We present a novel representation in the form of random walks over the design space, which facilitates both molecule generation and property prediction. We demonstrate clear advantages over existing methods in terms of performance, efficiency, and synthesizability of predicted molecules, and we provide detailed insights into the method's chemical interpretability.

Hierarchical Grammar-Induced Geometry for Data-Efficient Molecular Property Prediction

The prediction of molecular properties is a crucial task in the field of material and drug discovery. The potential benefits of using deep learning techniques are reflected in the wealth of recent literature. Still, these techniques are faced with a common challenge in practice: Labeled data are limited by the cost of manual extraction from literature and laborious experimentation. In this work, we propose a data-efficient property predictor by utilizing a learnable hierarchical molecular grammar that can generate molecules from grammar production rules. Such a grammar induces an explicit geometry of the space of molecular graphs, which provides an informative prior on molecular structural similarity. The property prediction is performed using graph neural diffusion over the grammar-induced geometry. On both small and large datasets, our evaluation shows that this approach outperforms a wide spectrum of baselines, including supervised and pre-trained graph neural networks. We include a detailed ablation study and further analysis of our solution, showing its effectiveness in cases with extremely limited data. Code is available at https://github.com/gmh14/Geo-DEG.

Adaptive Approximate Implicitization of Planar Parametric Curves via Weak Gradient Constraints

Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the problems of maintaining geometric features and choosing a reasonable implicit degree. The present paper has two contributions. We first introduce a new regularization constraint(called the weak gradient constraint) for both polynomial and non-polynomial curves, which efficiently possesses shape preserving. We then propose two adaptive algorithms of approximate implicitization for polynomial and non-polynomial curves respectively, which find the ``optimal'' implicit degree based on the behavior of the weak gradient constraint. More precisely, the idea is gradually increasing the implicit degree, until there is no obvious improvement in the weak gradient loss of the outputs. Experimental results have shown the effectiveness and high quality of our proposed methods.

Data-Efficient Graph Grammar Learning for Molecular Generation

The problem of molecular generation has received significant attention recently. Existing methods are typically based on deep neural networks and require training on large datasets with tens of thousands of samples. In practice, however, the size of class-specific chemical datasets is usually limited (e.g., dozens of samples) due to labor-intensive experimentation and data collection. This presents a considerable challenge for the deep learning generative models to comprehensively describe the molecular design space. Another major challenge is to generate only physically synthesizable molecules. This is a non-trivial task for neural network-based generative models since the relevant chemical knowledge can only be extracted and generalized from the limited training data. In this work, we propose a data-efficient generative model that can be learned from datasets with orders of magnitude smaller sizes than common benchmarks. At the heart of this method is a learnable graph grammar that generates molecules from a sequence of production rules. Without any human assistance, these production rules are automatically constructed from training data. Furthermore, additional chemical knowledge can be incorporated in the model by further grammar optimization. Our learned graph grammar yields state-of-the-art results on generating high-quality molecules for three monomer datasets that contain only ${\sim}20$ samples each. Our approach also achieves remarkable performance in a challenging polymer generation task with only $117$ training samples and is competitive against existing methods using $81$k data points. Code is available at https://github.com/gmh14/data_efficient_grammar.

Polygrammar: Grammar for Digital Polymer Representation and Generation

Polymers are widely-studied materials with diverse properties and applications determined by different molecular structures. It is essential to represent these structures clearly and explore the full space of achievable chemical designs. However, existing approaches are unable to offer comprehensive design models for polymers because of their inherent scale and structural complexity. Here, we present a parametric, context-sensitive grammar designed specifically for the representation and generation of polymers. As a demonstrative example, we implement our grammar for polyurethanes. Using our symbolic hypergraph representation and 14 simple production rules, our PolyGrammar is able to represent and generate all valid polyurethane structures. We also present an algorithm to translate any polyurethane structure from the popular SMILES string format into our PolyGrammar representation. We test the representative power of PolyGrammar by translating a dataset of over 600 polyurethane samples collected from literature. Furthermore, we show that PolyGrammar can be easily extended to the other copolymers and homopolymers such as polyacrylates. By offering a complete, explicit representation scheme and an explainable generative model with validity guarantees, our PolyGrammar takes an important step toward a more comprehensive and practical system for polymer discovery and exploration. As the first bridge between formal languages and chemistry, PolyGrammar also serves as a critical blueprint to inform the design of similar grammars for other chemistries, including organic and inorganic molecules.

Towards Evaluating and Training Verifiably Robust Neural Networks

Recent works have shown that interval bound propagation (IBP) can be used to train verifiably robust neural networks. Reseachers observe an intriguing phenomenon on these IBP trained networks: CROWN, a bounding method based on tight linear relaxation, often gives very loose bounds on these networks. We also observe that most neurons become dead during the IBP training process, which could hurt the representation capability of the network. In this paper, we study the relationship between IBP and CROWN, and prove that CROWN is always tighter than IBP when choosing appropriate bounding lines. We further propose a relaxed version of CROWN, linear bound propagation (LBP), that can be used to verify large networks to obtain lower verified errors than IBP. We also design a new activation function, parameterized ramp function (ParamRamp), which has more diversity of neuron status than ReLU. We conduct extensive experiments on MNIST, CIFAR-10 and Tiny-ImageNet with ParamRamp activation and achieve state-of-the-art verified robustness. Code and the appendix are available at https://github.com/ZhaoyangLyu/VerifiablyRobustNN.

Texture Memory-Augmented Deep Patch-Based Image Inpainting

Patch-based methods and deep networks have been employed to tackle image inpainting problem, with their own strengths and weaknesses. Patch-based methods are capable of restoring a missing region with high-quality texture through searching nearest neighbor patches from the unmasked regions. However, these methods bring problematic contents when recovering large missing regions. Deep networks, on the other hand, show promising results in completing large regions. Nonetheless, the results often lack faithful and sharp details that resemble the surrounding area. By bringing together the best of both paradigms, we propose a new deep inpainting framework where texture generation is guided by a texture memory of patch samples extracted from unmasked regions. The framework has a novel design that allows texture memory retrieval to be trained end-to-end with the deep inpainting network. In addition, we introduce a patch distribution loss to encourage high-quality patch synthesis. The proposed method shows superior performance both qualitatively and quantitatively on three challenging image benchmarks, i.e., Places, CelebA-HQ, and Paris Street-View datasets.