Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers’, and Navier-Stokes equations.
- Award ID(s):
- 1911836
- NSF-PAR ID:
- 10494469
- Editor(s):
- -
- Publisher / Repository:
- Journal of Engineering Mechanics
- Date Published:
- Journal Name:
- Journal of Engineering Mechanics
- Edition / Version:
- -
- Volume:
- 149
- Issue:
- 3
- ISSN:
- 0733-9399
- Subject(s) / Keyword(s):
- ["-"]
- Format(s):
- Medium: X Size: - Other: -
- Size(s):
- ["-"]
- Sponsoring Org:
- National Science Foundation
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Abstract -
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Abstract Ferromagnetic shape memory alloys (MSMAs), such as Ni-Mn-Ga single crystals, can exhibit the shape memory effect due to an applied magnetic field at room temperature. Under a variable magnetic field and a constant bias stress loading, MSMAs have been used for actuation applications. Under variable stress and a constant bias field, MSMAs can be used in power harvesting or sensing devices, e.g. in structural health monitoring applications. This behavior is primarily a result of the approximately tetragonal unit cell whose magnetic easy axis is approximately aligned with the short axis of the unit cell within the Ni-Mn-Ga single crystals. Under an applied field, the magnetic easy axis tends to align with the external field. Similarly, under an applied compressive force, the short side of the unit cell tends to align with the direction of the force. This work introduced a new feature to the existing macro-scale magneto-mechanical model for Ni-Mn-Ga single crystal. This model includes the fact that the magnetic easy axis in the two variants is not exactly perpendicular as observed by D’silva
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1061/JENMDT.EMENG-6901
