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Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions
Jihong Wang1, Xiaochuan Tian2, Zhongqiang Zhang3
1Department of Mathematics, Lehigh University, Bethlehem, 18015, PA, USA.
Computer Methods in Applied Mechanics and Engineering
|June 25, 2026
Summary
We introduce the monotone peridynamic neural operator (MPNO), a novel data-driven approach for learning nonlocal constitutive models. MPNO ensures solution uniqueness and exhibits superior generalization for complex material simulations.
Area of Science:
- Computational mechanics
- Materials science
- Machine learning
Background:
- Nonlocal continuum mechanics models like peridynamics are crucial for simulating complex materials.
- Current data-driven methods for peridynamics lack guaranteed well-posedness, leading to potential non-physical results.
- Accurate and reliable data-driven models are needed to streamline material characterization.
Purpose of the Study:
- To develop a data-driven nonlocal constitutive model with guaranteed well-posedness and solution uniqueness.
- To introduce the monotone peridynamic neural operator (MPNO) as a solution.
- To validate MPNO's performance on synthetic and real-world data.
Main Methods:
- MPNO learns a nonlocal kernel and constitutive relation using a monotone gradient network.
- This architectural constraint ensures the convexity of the learned energy density function.
- Guaranteed uniqueness of solutions in the small deformation regime is achieved.
Main Results:
- MPNO converges to the ground-truth model on synthetic data as measurement grid size decreases.
- MPNO demonstrates superior generalization compared to conventional neural networks on unseen data.
- MPNO successfully learns a homogenized model from molecular dynamics data, showing practical utility.
Conclusions:
- MPNO provides a robust framework for data-driven nonlocal material modeling with guaranteed well-posedness.
- The approach enhances accuracy and generalization in peridynamic simulations.
- MPNO offers a physically interpretable and expressive tool for materials science applications.
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