For a fixed number of measurements, the precision of standard addition depends on the measurement design, i.e., the selected spiking concentrations and the allocation of repeated measurements. This work derives practical design rules through a rigorous mathematical treatment. Using propagation of error, the estimator variance is approximated and its minimization is formulated as a c-optimality problem, which is then solved by applying Elfving’s theorem. This approach characterizes variance-optimal designs for a broad parametric class of non-decreasing variance functions, covering both homoscedastic and heteroscedastic settings. The variance-optimal design is uniquely supported on two concentration levels. These are the unspiked sample and a second concentration level determined by the variance structure and the admissible spiking range. When variance increases at most quadratically, the optimal added concentration equals the upper limit of this range. For faster variance growth, it may lie below this limit. A closed-form expression for the optimal allocation of repeated measurements is obtained, showing that it may deviate considerably from equal allocation depending on the variance structure and concentration range. In addition, weighted regression is shown to be unnecessary for any two-point standard addition design, thereby avoiding the need to determine suitable regression weights. Simulation studies demonstrate that, in the investigated settings with at most quadratic variance growth, even two-point designs with 50:50 allocation consistently outperform conventional multi-point designs with correctly weighted regression. Optimizing the allocation can provide substantial additional gains in precision. The corresponding implications for estimator bias are also assessed.
The optimization of the Bayer digestion process is critical for alumina production but is complicated by nonlinear mineral dissolution kinetics and the conflicting objectives of maximizing yield while minimizing caustic consumption. Traditional model-based optimization often fails in industrial practice because the objective—alkali consumption—is governed by complex side reactions (e.g., desilication products) that are difficult to model accurately (R2 = 0.34). To mitigate the risks associated with optimizing over such a flawed model surface, we propose a robust closed-loop decision framework. First, we construct a Nonlinear Auto Regressive with eXogenous inputs (NARX) soft sensor based on a pre-trained Transformer (R2 = 0.778) to capture complex process dynamics and residence time memory effects. Subsequently, to address the high epistemic uncertainty in the secondary objective, we formulate the optimization as a data-driven Chance-Constrained Programming (CCP) problem, deriving feasible regions directly from superior historical operations via Ideal Operating Zone Learning (IOZL). Based on historical ideal-zone comparison, the framework projected a 2.08% increase in dissolution rate and a 0.95% reduction in alkali consumption, providing a trustworthy pathway for intelligent control under model mismatch. This constraint learning architecture provides a practical risk-aware optimization strategy for chemical processes in which one or more objectives are difficult to model reliably. To facilitate reproducibility and industrial adoption, the source code and a reproducible decision-support prototype with quantified computational requirements are made available in the associated GitHub repository.
Asymmetric catalytic reactions play a critical role in the synthesis of enantiomerically enriched compounds, with broad applications in pharmaceuticals and fine chemicals. While recent advances in machine learning have improved reaction prediction using molecular descriptors and graph-based representations, existing approaches still face challenges such as limited generalizability, poor interpretability, and the scarcity of high-quality, domain-specific datasets. In this work, we propose CHIMERA, a chirality-augmented and molecular interaction-enhanced multi-level representation framework designed to improve both predictive accuracy and interpretability in asymmetric catalysis. CHIMERA integrates molecular fingerprints, graph-based molecular structures, and motif-decomposed graph embeddings within a hierarchical architecture. It incorporates a chirality-aware attention mechanism and a molecular interaction module to highlight atom-level contributions to reaction outcomes. To address data scarcity and distribution shifts, CHIMERA also introduces a domain adaptation module that enhances transferability across reaction types. We evaluate CHIMERA on two curated datasets of oxazoline-catalyzed asymmetric reactions. Experimental results show that CHIMERA outperforms existing baseline models in both predictive performance and interpretability, offering a promising tool for data-driven catalyst design and optimization in asymmetric synthesis.
