Designing complex computer-aided design (CAD) models is often time-consuming due to challenges such as computational inefficiency and the difficulty of generating precise models. We propose a novel language-guided framework for industrial design automation to address these issues, integrating large language models (LLMs) with computer-automated design (CAutoD).Through this framework, CAD models are automatically generated from parameters and appearance descriptions, supporting the automation of design tasks during the detailed CAD design phase. Our approach introduces three key innovations: (1) a semi-automated data annotation pipeline that leverages LLMs and vision-language large models (VLLMs) to generate high-quality parameters and appearance descriptions; (2) a Transformer-based CAD generator (TCADGen) that predicts modeling sequences via dual-channel feature aggregation; (3) an enhanced CAD modeling generation model, called CADLLM, that is designed to refine the generated sequences by incorporating the confidence scores from TCADGen. Experimental results demonstrate that the proposed approach outperforms traditional methods in both accuracy and efficiency, providing a powerful tool for automating industrial workflows and generating complex CAD models from textual prompts.The code is available at https://jianxliao.github.io/cadllm-page/

With the proliferation of artificial intelligence, Computer-Aided Design (CAD) is being transformed into Computer-Automated Design (CAutoD). In this paper, the advent of Large Language Models (LLMs) introduces new opportunities for CAutoD. This study develops AutoForma, an LLM-based multi-agent system, for automatic conversion from natural language descriptions to 3D models. By harnessing the comprehension capabilities of LLMs, AutoForma streamlines the CAutoD workflow by efficiently translating design intents into precise models in CAD. Through a comprehensive set of evaluations, AutoForma is seen to offer automation performance across various design tasks, particularly in generating non-standard parts that meet specific requirements, with higher efficiency and accuracy than using just an LLM like GPT-4.

Graph Knowledge Distillation (GKD) in artificial intelligence typically employs a teacher-student model, which faces challenges such as rigidity, time-consumption, and teacher training. To improve, this paper develops a Graph self-Distillation Network (GraDiNet), a framework that operates without the need for a teacher model or graph neural network (GNN) during training and inferencing phases. GraDiNet uniquely utilizes multi-layer perceptrons (MLPs) to harness both the structural knowledge of graphs and the semantic information of nodes, thus facilitating hierarchical self-distillation between a target node and its neighbors. Additionally, the GraDiNet approach incorporates a novel similarity-based difference enhancement technique and a penalty factor within the training loss to further delineate the distinction between positive and negative samples. This allows GraDiNet not only to bypass the necessity for a GNN teacher in learning graph structure knowledge but also to predict node classification efficiently. Extensive evaluations show that standard MLPs can significantly boost their performance through this implicit hierarchical self-distillation and the similarity difference enhancement. GraDiNet thus achieves an average improvement of 15% over conventional MLPs and outperforms leading state-of-the-art GKD methods across three real-world datasets.

Inspired by a mathematical riddle involving fuses, we define the "fusible numbers" as follows: $0$ is fusible, and whenever $x,y$ are fusible with $|y-x|<1$, the number $(x+y+1)/2$ is also fusible. We prove that the set of fusible numbers, ordered by the usual order on $\mathbb R$, is well-ordered, with order type $\varepsilon_0$. Furthermore, we prove that the density of the fusible numbers along the real line grows at an incredibly fast rate: Letting $g(n)$ be the largest gap between consecutive fusible numbers in the interval $[n,\infty)$, we have $g(n)^{-1} \ge F_{\varepsilon_0}(n-c)$ for some constant $c$, where $F_\alpha$ denotes the fast-growing hierarchy. Finally, we derive some true statements that can be formulated but not proven in Peano Arithmetic, of a different flavor than previously known such statements: PA cannot prove the true statement "For every natural number $n$ there exists a smallest fusible number larger than $n$." Also, consider the algorithm "$M(x)$: if $x<0$ return $-x$, else return $M(x-M(x-1))/2$." Then $M$ terminates on real inputs, although PA cannot prove the statement "$M$ terminates on all natural inputs."

Inspired by a mathematical riddle involving fuses, we define the fusible numbers as follows: 0 is fusible, and whenever x, y are fusible with |y - x|- 1≥ Fε0(n - c) for some constant c, where Fα denotes the fast-growing hierarchy.Finally, we derive some true statements that can be formulated but not proven in Peano Arithmetic, of a different flavor than previously known such statements: PA cannot prove the true statement "For every natural number n there exists a smallest fusible number larger than n." Also, consider the algorithm "M(x): if x <; 0 return -x, else return M(x - M(x - 1))/2." Then M terminates on real inputs, although PA cannot prove the statement "M terminates on all natural inputs."

We consider optimal two-impulse space interception problems with multiple constraints. The multiple constraints are imposed on the terminal position of a space interceptor, impulse and impact instants, and the component-wise magnitudes of velocity impulses. These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations. Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used. A new dynamic slackness variable method is presented. As a result, an indirect optimization method is developed. Subsequently, our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles. A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions. Specifically, by numerical examples, we show that when time and velocity impulse constraints are imposed, optimal two-impulse solutions may occur; if two-impulse instants are free, then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.

Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the Hohmann transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality constraint. By the Kuhn-Tucker theorem and a second-order sufficient condition for minima, we analytically prove the global minimum of the Hohmann transfer. Two sets of feasible solutions are found: one corresponding to the Hohmann transfer is the global minimum and the other is a local minimum. We next formulate the Hohmann transfer problem as boundary value problems, which are solved by the calculus of variations. The two sets of feasible solutions are also found by numerical examples. Via static and dynamic constrained optimizations, the solution to the Hohmann transfer problem is re-discovered, and its global minimum is analytically verified using nonlinear programming.