mlsanityData to 14 Oct 2026

DUE: A Deep Learning Framework and Library for Modeling Unknown Equations

arXiv 2504.10373 ↗First posted 14 Apr 2025cs.LG cs.NA math.DScited by 8

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Abstract (arXiv)

Equations, particularly differential equations, are fundamental for understanding natural phenomena and predicting complex dynamics across various scientific and engineering disciplines. However, the governing equations for many complex systems remain unknown due to intricate underlying mechanisms. Recent advancements in machine learning and data science offer a new paradigm for modeling unknown equations from measurement or simulation data. This paradigm shift, known as data-driven discovery or modeling, stands at the forefront of AI for science, with significant progress made in recent years. In this paper, we introduce a systematic framework for data-driven modeling of unknown equations using deep learning. This versatile framework is capable of learning unknown ODEs, PDEs, DAEs, IDEs, SDEs, reduced or partially observed systems, and non-autonomous differential equations. Based on this framework, we have developed Deep Unknown Equations (DUE), an open-source software package designed to facilitate the data-driven modeling of unknown equations using modern deep learning techniques. DUE serves as an educational tool for classroom instruction, enabling students and newcomers to gain hands-on experience with differential equations, data-driven modeling, and contemporary deep learning approaches such as FNN, ResNet, generalized ResNet, operator semigroup networks (OSG-Net), and Transformers. Additionally, DUE is a versatile and accessible toolkit for researchers across various scientific and engineering fields. It is applicable not only for learning unknown equations from data but also for surrogate modeling of known, yet complex, equations that are costly to solve using traditional numerical methods. We provide detailed descriptions of DUE and demonstrate its capabilities through diverse examples, which serve as templates that can be easily adapted for other applications.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 44 of its 70 references that are in the map. First posted on arXiv 14 Apr 2025.

Builds on

44 of 70 references.

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32 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 6.

8 papers.

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  2. 2026Hypothesis-driven construction of mesoscopic dynamicscited by 2
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  4. 2026MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Datacited by 1
  5. 2026CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systemscited by 1
  6. 2025A Hybrid Framework for Healing Semigroups with Machine Learningcited by 0
  7. 2026Time-Delayed Transformers for Data-Driven Modeling of Low-Dimensional Dynamicscited by 0
  8. 2026Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solvercited by 0