Future events such as the weather or satellite trajectories are computed in tiny time steps, so the computation must be both efficient and as accurate as possible at each step lest errors pile up. A Kobe University team now introduces a new method that uses deep learning for creating tailored, accurate simulations that respect physical laws, while also being more computationally efficient.
To simulate the behavior of physical systems more accurately than ever, Kobe University YAGUCHI Takaharu and his team have developed an approach that can learn physically accurate computation methods based on a broad range of target data (blue: ground truth; yellow: previous accurate simulation; red: new approach). © Kobe University (CC BY-SA)
From studying the behavior of atoms to setting the trajectory of space craft, from material development to weather prediction — the modern world depends on computer simulations. Their computation proceeds time step by time step, and as each step is just an approximation, even the tiniest inaccuracies compound into significant errors at larger time scales. Kobe University machine learning expert YAGUCHI Takaharu explains: “Recently, deep learning methods are beginning to be used, but they often violate physical laws needed for accuracy. More traditional physical simulations may be more accurate; however, they are very time- and resource-intensive.”
Yaguchi has 20 years of experience developing physical simulations that preserve principles such as the law of conservation of energy. Together with the Norwegian University of Science and Technology, he was therefore looking for an approach that combines the accuracy of methods that respect physical laws and the efficiency of deep learning.
At the Thirty-Ninth Annual Conference on Neural Information Processing Systems (NeurIPS 2025) Yaguchi’s team now presents that they found a way of learning energy-behavior-preserving and therefore highly accurate time step computation from target data. And not only did they show mathematically that their method would obey key physical laws, they also demonstrate the superior accuracy of their method in sample simulations of a broad range of typical physical systems. “Methods created this way achieve a degree of precision for simulating the long-term prediction of diverse phenomena, even of those exhibiting chaotic behavior, that is difficult for humans to design manually. What’s particularly significant is that the approach yields methods tailored towards the system of interest, from materials development to weather forecasting,” explains Yaguchi.
The researchers did not fail to also consider the required computational resources. They found that their new approach only took about 70% of the computation time of the next most accurate, conventional computation method. Yaguchi says, “Our proposed approach can therefore compute more accurate solutions in shorter time, and that includes the time required for generating the test data and training the model on it.”
Yaguchi is looking at the future with great expectations, saying: “If we manage to endow this method with an additional property called ‘symplecticity,’ it may also enable simulations of energy-preserving systems almost entirely free of error. Creating such a method was previously believed impossible, but our approach could make it achievable.”
Simulation of the stellar motion in a plane with the Hénon-Heiles model as an example: Compared to various alternative simulation approaches (third to sixth from left), the approach developed by YAGUCHI Takaharu and his team (second from left) is closest to the true long-term behavior of physical systems (leftmost). This can also be seen as the error (rightmost) being smallest (colors in the “global error” plot correspond to colors in the different model plots). © E. Celledoni et al., Advances in Neural Information Processing Systems 2025 (DOI TBD) (CC BY-SA)
Acknowledgements
This research was funded by the Japan Science and Technology Agency (grants JPMJCR1914, JPMJCR24Q5, JPMJAP2329), the Japan Society for the Promotion of Science (grant 25K15148) and the National Institute for Fusion Science (grant NIFS25KISC015). It was conducted in collaboration with researchers from the Norwegian University of Science and Technology under the Horizon Europe MSCA staff exchanges project “REMODEL – Research exchanges in the mathematics of deep learning with applications” and the RIKEN Center for Advanced Intelligence Project.
Original publication
E. Celledoni et al.: UEPI: Universal Energy-Behavior-Preserving Integrators for Energy Conservative/Dissipative Differential Equations. Advances in Neural Information Processing Systems (2025). DOI:
Release on EurekAlert!
Making simulations more accurate than ever with deep learning
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