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Critique of De-Facto Standard Loss Functions for Force-Field Training: Why Energy–Force Balance Fails on Anharmonic Systems
The de-facto standard loss function employed in training machine learning interatomic potentials consists of a weighted combination of the mean squared error on total energies and the mean squared error on atomic forces. Researchers routinely adjust the relative weights assigned to energy and force terms in an attempt to achieve an optimal balance between these two objectives. This practice rests on the core assumption that energy errors and force errors maintain a simple linear relationship across all relevant atomic configurations. The present critique demonstrates that this assumption collapses when the loss function is applied to anharmonic systems where large-amplitude vibrations thermal disorder or phase-transition pathways dominate material behaviour. Four distinct failure modes are identified: harmonic bias force overfitting energy drift and extrapolation collapse. Each mode arises directly from the mismatch between the loss-function design and the non-quadratic nature of anharmonic potential-energy surfaces. Harmonic bias occurs because the weighted loss preferentially rewards models that reproduce quadratic energy landscapes typical of small-displacement training data even when those models are later deployed at elevated temperatures. Force overfitting emerges when the high-dimensional force term receives excessive weight causing the model to memorise training-set force patterns that do not generalise to unexplored configurational space. Energy drift follows because the balance achieved at zero-kelvin conditions no longer holds once thermal fluctuations populate regions of the energy surface far from the training distribution. Extrapolation collapse completes the picture because the loss function provides no explicit penalty for predictions outside the narrow domain of the training data rendering the model unusable for high-temperature properties. These failures have direct consequences for the prediction of thermal transport coefficients phonon lifetimes and finite-temperature stability in materials ranging from high-entropy alloys to solid electrolytes. The critique concludes by outlining detection principles and mitigation strategies that move beyond the energy–force balance paradigm advocating instead for anharmonic-aware loss designs that explicitly incorporate temperature-dependent information and higher-order derivatives. Adoption of such designs is essential if machine learning force fields are to deliver reliable predictions for the thermally activated processes that govern real-world materials performance.
Journal of Computational and Data-Driven Materials Engineering
Original Research | Open access | 18 January 2026 | Article: 70
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