Designing physical artifacts that serve a purpose---such as tools and other functional structures---is central to engineering as well as everyday human behavior. Though automating design using machine learning has tremendous promise, existing methods are often limited by the task-dependent distributions they were exposed to during training.

Physics-informed neural networks (PINNs) have emerged as a promising approach for solving complex fluid dynamics problems, yet their application to fluid-structure interaction (FSI) problems with moving boundaries remains largely unexplored. This work addresses the critical challenge of modeling FSI systems with moving interfaces, where traditional unified PINN architectures struggle to capture the distinct physics governing fluid and structural domains simultaneously. We present an innovative Eulerian-Lagrangian PINN architecture that integrates immersed boundary method (IBM) principles to solve FSI problems with moving boundary conditions. Our approach fundamentally departs from conventional unified architectures by introducing domain-specific neural networks: an Eulerian network for fluid dynamics and a Lagrangian network for structural interfaces, coupled through physics-based constraints. Additionally, we incorporate learnable B-spline activation functions with SiLU to capture both localized high-gradient features near interfaces and global flow patterns. Empirical studies on a 2D cavity flow problem involving a moving solid structure show that while baseline unified PINNs achieve reasonable velocity predictions, they suffer from substantial pressure errors (12.9%) in structural regions. Our Eulerian-Lagrangian architecture with learnable activations (EL-L) achieves better performance across all metrics, improving accuracy by 24.1-91.4% and particularly reducing pressure errors from 12.9% to 2.39%. These results demonstrate that domain decomposition aligned with physical principles, combined with locality-aware activation functions, is essential for accurate FSI modeling within the PINN framework.

Designing physical artifacts that serve a purpose---such as tools and other functional structures---is central to engineering as well as everyday human behavior. Though automating design using machine learning has tremendous promise, existing methods are often limited by the task-dependent distributions they were exposed to during training. This constitutes a simple, fast, and reusable approach that solves high-dimensional problems with complex physical dynamics, including designing surfaces and tools to manipulate fluid flows and optimizing the shape of an airfoil to minimize drag. This framework produces high-quality designs by propagating gradients through trajectories of hundreds of steps, even when using models that were pre-trained for single-step predictions on data substantially different from the design tasks. In our fluid manipulation tasks, the resulting designs outperformed those found by sampling-based optimization techniques.

Designing physical artifacts that serve a purpose---such as tools and other functional structures---is central to engineering as well as everyday human behavior. Though automating design using machine learning has tremendous promise, existing methods are often limited by the task-dependent distributions they were exposed to during training. This constitutes a simple, fast, and reusable approach that solves high-dimensional problems with complex physical dynamics, including designing surfaces and tools to manipulate fluid flows and optimizing the shape of an airfoil to minimize drag. This framework produces high-quality designs by propagating gradients through trajectories of hundreds of steps, even when using models that were pre-trained for single-step predictions on data substantially different from the design tasks. In our fluid manipulation tasks, the resulting designs outperformed those found by sampling-based optimization techniques.

The primary aim of this study is to enhance the accuracy of our aerodynamic Fluid-Structure Interaction (FSI) model to support the controlled tracking of 3D flight trajectories by Aerobat, which is a dynamic morphing winged drone. Building upon our previously documented Unsteady Aerodynamic model rooted in horseshoe vortices, we introduce a new iteration of Aerobat, labeled as version beta, which is designed for attachment to a Kinova arm. Through a series of experiments, we gather force-moment data from the robotic arm attachment and utilize it to fine-tune our unsteady model for banking turn maneuvers. Subsequently, we employ the tuned FSI model alongside a collocation control strategy to accomplish 3D banking turns of Aerobat within simulation environments. The primary contribution lies in presenting a methodical approach to calibrate our FSI model to predict complex 3D maneuvers and successfully assessing the model's potential for closed-loop flight control of Aerobat using an optimization-based collocation method.

A mesh motion model based on deep operator networks is presented. The model is trained on and evaluated against a biharmonic mesh motion model on a fluid-structure interaction benchmark problem and further evaluated in a setting where biharmonic mesh motion fails. The performance of the proposed mesh motion model is comparable to the biharmonic mesh motion on the test problems.