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Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering…
Multimodal protein language models (PLMs) integrate sequence and token-based structural information, serving as a powerful foundation for protein modeling, generation, and design. However, the reliance on tokenizing 3D structures into…
In this paper, we will first introduce a novel multiscale representation (MSR) for shapes. Based on the MSR, we will then design a surface inpainting algorithm to recover 3D geometry of blood vessels. Because of the nature of irregular…
We present a system that allows users to visualize complex human motion via 3D motion sculptures---a representation that conveys the 3D structure swept by a human body as it moves through space. Given an input video, our system computes the…
In this dissertation, we concentrate on the challenging research issue of developing a spline-based modeling framework, which converts the conventional data (e.g., surface meshes) to tensor-product trivariate splines. This methodology can…
The representation space of pretrained Language Models (LMs) encodes rich information about words and their relationships (e.g., similarity, hypernymy, polysemy) as well as abstract semantic notions (e.g., intensity). In this paper, we…
Three-dimensional Morphable Models (3DMMs) are powerful statistical tools for representing the 3D surfaces of an object class. In this context, we identify an interesting question that has previously not received research attention: is it…
Template 3D shapes are useful for many tasks in graphics and vision, including fitting observation data, analyzing shape collections, and transferring shape attributes. Because of the variety of geometry and topology of real-world shapes,…
Creating and editing the shape and color of 3D objects require tremendous human effort and expertise. Compared to direct manipulation in 3D interfaces, 2D interactions such as sketches and scribbles are usually much more natural and…
Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…
The representation of workflows and processes is essential in materials science engineering, where experimental and computational reproducibility depend on structured and semantically coherent process models. Although numerous ontologies…
Physics-based simulation underpins engineering analysis but remains difficult to deploy in practice due to complex setup, parameterization, and interpretation. While Large Language Model-based agentic systems have shown promise in…
Automated methods for discovering mechanistic simulator models from observational data offer a promising path toward accelerating scientific progress. Such methods often take the form of agentic-style iterative workflows that repeatedly…
The advent of large language models, enabling flexibility through instruction-driven approaches, has revolutionized many traditional generative tasks, but large models for 3D data, particularly in comprehensively handling 3D shapes with…
In this paper we show by using the example of UML, how a software engineering method can benefit from an integrative mathematical foundation. The mathematical foundation is given by a mathematical system model. This model provides the basis…
Humans naturally understand 3D spatial relationships, enabling complex reasoning like predicting collisions of vehicles from different directions. Current large multimodal models (LMMs), however, lack of this capability of 3D spatial…
Proteins adopt multiple structural conformations to perform their diverse biological functions, and understanding these conformations is crucial for advancing drug discovery. Traditional physics-based simulation methods often struggle with…
Large Language Models are increasingly capable of interpreting multimodal inputs to generate complex 3D shapes, yet robust methods to evaluate geometric and structural fidelity remain underdeveloped. This paper introduces a human in the…
Point clouds have recently gained interest, especially for real-time applications and for 3D-scanned material, such as is used in autonomous driving, architecture, and engineering, to model real estate for renovation or display. Point…
As space exploration advances, underground environments are becoming increasingly attractive due to their potential to provide shelter, easier access to resources, and enhanced scientific opportunities. Although such environments exist on…