Accurate prediction is not profitable advice: profit-based evaluation of machine learning nitrogen recommendations in winter wheat
Xulong WangPo Yang
Aug 2026
Machine Learning
Abstract
Nitrogen rates for winter wheat are set before the season, under unknown prices and weather. The standard UK advice does not respond to prices, yet recent price swings moved the most profitable rate by tens of kilograms per hectare. Machine learning is often proposed as the fix. However, it is usually judged on prediction accuracy, and accurate prediction does not by itself make the recommended rate more profitable. Our insight is to score nitrogen advice directly by the profit it forgoes on measured yield response curves. We build a test bench on 892 such curves from two long running UK experiments, and sweep the nitrogen to grain price ratio to cover all price scenarios. On this bench, machine learning fails as a predictor. No model recovers the best rate within farm tolerance, and the benchmark noise shows none can. At normal prices, every model also loses to the standard advice on profit. The gain sits elsewhere. A simple correction step applied after the model cuts profit losses by a quarter, while better models and extra features give no gain. The same frozen correction cuts losses by 43% at the second site without any retraining. A hybrid of standard advice plus a damped correction removes bias and trims rare large losses. The same price sweep also prices emission cuts, at a cost comparable to current carbon prices. Machine learning therefore pays as a profit scored correction to standard advice, not as its replacement.
This article investigates several physics-informed and hybrid machine learning strategies that incorporate physics knowledge in experimental data-driven deep-learning models for predicting the bond quality and porosity of fused filament fabrication (FFF) parts. Three types of strategies are explored to incorporate physics constraints and multi-physics FFF simulation results into a deep neural network (DNN), thus ensuring consistency with physical laws: (1) incorporate physics constraints within the loss function of the DNN, (2) use physics model outputs as additional inputs to the DNN model, and (3) pre-train a DNN model with physics model input-output and then update it with experimental data. These strategies help to enforce a physically consistent relationship between bond quality and tensile strength, thus making porosity predictions physically meaningful. Eight different combinations of the above strategies are investigated. The results show how the combination of multiple strategies produces accurate machine learning models even with limited experimental data.
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