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[2505.21723] Are Statistical Methods Obsolete in the Era of Deep Learning? A Study of ODE Inverse Problems
Summary
This article examines the relevance of statistical methods in the age of deep learning, using ordinary differential equation (ODE) inverse problems as a case study. It highlights the strengths of statistical approaches compared to deep learning models in various scenarios.
Why It Matters
As deep learning continues to dominate the AI landscape, understanding the comparative effectiveness of traditional statistical methods is crucial for researchers and practitioners. This study demonstrates that statistical methods remain vital, particularly in scenarios with sparse data and noisy observations, challenging the notion of their obsolescence.
Key Takeaways
- Statistical methods are not obsolete; they often outperform deep learning in specific contexts.
- In scenarios with sparse and noisy data, statistical methods achieve lower bias and variance.
- Statistical approaches require fewer parameters and less hyperparameter tuning compared to deep learning models.
- They demonstrate greater robustness against numerical imprecision and better fidelity to underlying systems.
- Statistical methods excel in out-of-sample predictions where deep learning may falter.
Statistics > Computation arXiv:2505.21723 (stat) [Submitted on 27 May 2025 (v1), last revised 14 Feb 2026 (this version, v2)] Title:Are Statistical Methods Obsolete in the Era of Deep Learning? A Study of ODE Inverse Problems Authors:Skyler Wu, Shihao Yang, S. C. Kou View a PDF of the paper titled Are Statistical Methods Obsolete in the Era of Deep Learning? A Study of ODE Inverse Problems, by Skyler Wu and 2 other authors View PDF HTML (experimental) Abstract:In the era of AI, neural networks have become increasingly popular for modeling, inference, and prediction, largely due to their potential for universal approximation. With the proliferation of such deep learning models, a question arises: are leaner statistical methods still relevant? To shed insight on this question, we employ the mechanistic nonlinear ordinary differential equation (ODE) inverse problem as a testbed, using the physics-informed neural network (PINN) as a representative of the deep learning paradigm and manifold-constrained Gaussian process inference (MAGI) as a representative of statistically principled methods. Through case studies involving the SEIR model from epidemiology and the Lorenz model from chaotic dynamics, we demonstrate that statistical methods are far from obsolete, especially when working with sparse and noisy observations. On tasks such as parameter inference and trajectory reconstruction, statistically principled methods consistently achieve lower bias and variance, while using far...
