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Modeling fluid flow and transport in heterogeneous systems is often challenged by unknown parameters that vary in space. In inverse modeling, measurement data are used to estimate these parameters. Due to the spatial variability of these unknown parameters in heterogeneous systems (e.g., permeability or diffusivity), the inverse problem is ill-posed and infinite solutions are possible. Physics-informed neural networks (PINN) have become a popular approach for solving inverse problems. However, in inverse problems in heterogeneous systems, PINN can be sensitive to hyperparameters and can produce unrealistic patterns. Motivated by the concept of ensemble learning and variance reduction in machine learning, we propose an ensemble PINN (ePINN) approach where an ensemble of parallel neural networks is used and each sub-network is initialized with a meaningful pattern of the unknown parameter. Subsequently, these parallel networks provide a basis that is fed into a main neural network that is trained using PINN. It is shown that an appropriately selected set of patterns can guide PINN in producing more realistic results that are relevant to the problem of interest. To assess the accuracy of this approach, inverse transport problems involving unknown heat conductivity, porous media permeability, and velocity vector fields were studied. The proposed ePINN approach was shown to increase the accuracy in inverse problems and mitigate the challenges associated with non-uniqueness.
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This content will become publicly available on August 17, 2026
Ellipse Synthesis of the Planar 2R Using Convolutional Neural Networks
The transmission properties of multi-degree-of-freedom mechanisms can be tuned by shaping velocity ellipses throughout their workspace. Velocity ellipses are the image of a circle in the actuator velocity space mapped by the Jacobian into end-effector velocities. In this work, two machine learning methods using convolutional neural network architectures are proposed to synthesize planar 2R mechanism designs that approximately produce the desired velocity ellipses. An ensemble of image-based regression models is trained in a supervised fashion to output multiple 2R designs that approximate the specified ellipses. As an alternative to this approach, a second physics-informed neural network is constructed to train an ensemble of encoder models without specifying the 2R link lengths. During training, a decoder model that approximates the kinematics (physics) of the 2R is used to find how well the 2R design output by the encoder approximates the specified ellipses. These models are used to obtain multiple 2R designs that produce ellipses suitable for legged locomotion tasks and some preliminary results are presented.
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- Award ID(s):
- 2144732
- PAR ID:
- 10656472
- Publisher / Repository:
- ASME Digital Collection
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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