In the high-cost simulation-driven design domain, translating ambiguous design requirements into a mathematical optimization formulation is a bottleneck for optimizing product performance. This process is time-consuming and heavily reliant on expert knowledge. While large language models (LLMs) offer potential for automating this task, existing approaches either suffer from poor formalization that fails to accurately align with the design intent or rely on solver feedback for data filtering, which is unavailable due to the high simulation costs. To address this challenge, we propose automated problem formulation (APF), a solver-independent framework that utilizes LLMs to convert engineers’ natural language requirements into executable optimization models. The core of this framework is an innovative pipeline for automatically generating high-quality data, which overcomes the difficulty of constructing suitable fine-tuning datasets in the absence of high-cost solver feedback with the help of data generation and test instance annotation. The generated high-quality dataset is used to perform supervised fine-tuning on LLMs, significantly enhancing their ability to generate accurate and executable optimization problem formulations. Experimental results on antenna design demonstrate that APF significantly outperforms the existing methods in both the accuracy of requirement formalization and the quality of resulting radiation efficiency curves in meeting the design goals.

Incorporating syntax into neural approaches in NLP has a multitude of practical and scientific benefits. For instance, a language model that is syntax-aware is likely to be able to produce better samples; even a discriminative model like BERT with a syntax module could be used for core NLP tasks like unsupervised syntactic parsing. Rapid progress in recent years was arguably spurred on by the empirical success of the Parsing-Reading-Predict architecture of (Shen et al., 2018a), later simplified by the Order Neuron LSTM of (Shen et al., 2019). Most notably, this is the first time neural approaches were able to successfully perform unsupervised syntactic parsing (evaluated by various metrics like F-1 score). However, even heuristic (much less fully mathematical) understanding of why and when these architectures work is lagging severely behind. In this work, we answer representational questions raised by the architectures in (Shen et al., 2018a, 2019), as well as some transition-based syntax-aware language models (Dyer et al., 2016): what kind of syntactic structure can current neural approaches to syntax represent? Concretely, we ground this question in the sandbox of probabilistic context-free-grammars (PCFGs), and identify a key aspect of the representational power of these approaches: the amount and directionality of context that the predictor has access to when forced to make parsing decision. We show that with limited context (either bounded, or unidirectional), there are PCFGs, for which these approaches cannot represent the max-likelihood parse; conversely, if the context is unlimited, they can represent the max-likelihood parse of any PCFG.