# A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database

arXiv: https://arxiv.org/abs/1907.12651 · HTML: https://mlsanity.com/paper/1907.12651/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2019.

## Built on by (most cited first, 18 of 18)

- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
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- [Deep autoencoders for physics-constrained data-driven nonlinear materials modeling](https://mlsanity.com/paper/2209.04416/) (2022)
- [Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity](https://mlsanity.com/paper/2208.00246/) (2022)
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- [A Neural Network-enhanced Reproducing Kernel Particle Method for Modeling Strain Localization](https://mlsanity.com/paper/2204.13821/) (2022)
- [LS-DYNA Machine Learning-based Multiscale Method for Nonlinear Modeling of Short Fiber-Reinforced Composites](https://mlsanity.com/paper/2301.02738/) (2023)
- [A Multi-Resolution Physics-Informed Recurrent Neural Network: Formulation and Application to Musculoskeletal Systems](https://mlsanity.com/paper/2305.16593/) (2023)
- [History-Aware Neural Operator: Robust Data-Driven Constitutive Modeling of Path-Dependent Materials](https://mlsanity.com/paper/2506.10352/) (2025)
- [A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture](https://mlsanity.com/paper/2307.01937/) (2023)
- [Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanics](https://mlsanity.com/paper/2311.12915/) (2023)
- [Cell division in deep material networks applied to multiscale strain localization modeling](https://mlsanity.com/paper/2101.07226/) (2021)
- [Manifold embedding data-driven mechanics](https://mlsanity.com/paper/2112.09842/) (2021)
- [Differentiable Neural-Integrated Meshfree Method for Forward and Inverse Modeling of Finite Strain Hyperelasticity](https://mlsanity.com/paper/2407.11183/) (2024)
- [N-Adaptive Ritz Method: A Neural Network Enriched Partition of Unity for Boundary Value Problems](https://mlsanity.com/paper/2401.08544/) (2024)
- [Data-Driven Modeling of an Unsaturated Bentonite Buffer Model Test Under High Temperatures Using an Enhanced Axisymmetric Reproducing Kernel Particle Method](https://mlsanity.com/paper/2309.13519/) (2023)
- [Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modeling](https://mlsanity.com/paper/2602.07192/) (2026)

## Abstract (arXiv)

Physics-constrained data-driven computing is an emerging hybrid approach that integrates universal physical laws with data-driven models of experimental data for scientific computing. A new data-driven simulation approach coupled with a locally convex reconstruction, termed the local convexity data-driven (LCDD) computing, is proposed to enhance accuracy and robustness against noise and outliers in data sets in the data-driven computing. In this approach, for a given state obtained by the physical simulation, the corresponding optimum experimental solution is sought by projecting the state onto the associated local convex manifold reconstructed based on the nearest experimental data. This learning process of local data structure is less sensitive to noisy data and consequently yields better accuracy. A penalty relaxation is also introduced to recast the local learning solver in the context of non-negative least squares that can be solved effectively. The reproducing kernel approximation with stabilized nodal integration is employed for the solution of the physical manifold to allow reduced stress-strain data at the discrete points for enhanced effectiveness in the LCDD learning solver. Due to the inherent manifold learning properties, LCDD performs well for high-dimensional data sets that are relatively sparse in real-world engineering applications. Numerical tests demonstrated that LCDD enhances nearly one order of accuracy compared to the standard distance-minimization data-driven scheme when dealing with noisy database, and a linear exactness is achieved when local stress-strain relation is linear.