Publications

2024

1. Patent

   Vibration attenuation via tailored metastructures

   Fabio Semperlotti ,  Mehdi Jokar ,  and  Siddharth Nair

   2024

   US Patent App. 18/217,539

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   The vibration attenuation system includes a load bearing layer, a non-load bearing layer, and a rigid beam connector. The load bearing layer has a first density and a first stiffness. The non-load bearing layer has a second density and a second stiffness. The second density is lower than the first density. The rigid beam connector has a third density and a third stiffness. The rigid beam connector couples the load bearing layer to the non-load bearing layer. The coupling of the non-load bearing layer to the load bearing layer is enabled through the use of the rigid beam connector which provides a nonlocal connection to transfer energy from the load bearing layer to the non-load bearing layer.

   @misc{semperlotti2024vibration,
     title = {Vibration attenuation via tailored metastructures},
     author = {Semperlotti, Fabio and Jokar, Mehdi and Nair, Siddharth},
     year = {2024},
     publisher = {Google Patents},
     note = {US Patent App. 18/217,539},
   }

2. arXiv

   Time transient Simulations via Finite Element Network Analysis: Theoretical Formulation and Numerical Validation

   Mehdi Jokar ,  Siddharth Nair ,  and  Fabio Semperlotti

   arXiv preprint arXiv:2407.02494, 2024

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   This paper extends the finite element network analysis (FENA) to include a dynamic time-transient formulation. FENA was initially formulated in the context of the linear static analysis of 1D and 2D elastic structures. By introducing the concept of super finite network element, this paper provides the necessary foundation to extend FENA to linear time-transient simulations for both homogeneous and inhomogeneous domains. The concept of neural network concatenation, originally formulated to combine networks representative of different structural components in space, is extended to the time domain. Network concatenation in time enables training neural network models based on data available in a limited time frame and then using the trained networks to simulate the system evolution beyond the initial time window characteristic of the training data set. The proposed methodology is validated by applying FENA to the transient simulation of one-dimensional structural elements (such as rods and beams) and by comparing the results with either analytical or finite element solutions. Results confirm that FENA accurately predicts the dynamic response of the physical system and, while introducing an error on the order of 1% (compared to analytical or computational solutions of the governing differential equations), it is capable of delivering extreme computational efficiency.

   @article{jokar2024time,
     title = {Time transient Simulations via Finite Element Network Analysis: Theoretical Formulation and Numerical Validation},
     author = {Jokar, Mehdi and Nair, Siddharth and Semperlotti, Fabio},
     journal = {arXiv preprint arXiv:2407.02494},
     year = {2024},
   }

3. SPIE-2024

   Acoustic scattering simulations via physics-informed neural network

   Siddharth Nair ,  Timothy F Walsh ,  Gregory Pickrell ,  and  Fabio Semperlotti

   In Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2024 , 2024

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   Multiple scattering is a common phenomenon in acoustic media that arises from the interaction of the acoustic field with a network of scatterers. This mechanism is dominant in problems such as the design and simulation of acoustic metamaterial structures often used to achieve acoustic control for sound isolation, and remote sensing. In this study, we present a physics-informed neural network (PINN) capable of simulating the propagation of acoustic waves in an infinite domain in the presence of multiple rigid scatterers. This approach integrates a deep neural network architecture with the mathematical description of the physical problem in order to obtain predictions of the acoustic field that are consistent with both governing equations and boundary conditions. The predictions from the PINN are compared with those from a commercial finite element software model in order to assess the performance of the method.

   @inproceedings{nair2024acoustic,
     title = {Acoustic scattering simulations via physics-informed neural network},
     author = {Nair, Siddharth and Walsh, Timothy F and Pickrell, Gregory and Semperlotti, Fabio},
     booktitle = {Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2024},
     volume = {12949},
     pages = {138--145},
     year = {2024},
     organization = {SPIE},
   }

4. arXiv

   Physics and geometry informed neural operator network with application to acoustic scattering

   Siddharth Nair ,  Timothy F Walsh ,  Greg Pickrell ,  and  Fabio Semperlotti

   arXiv preprint arXiv:2406.03407, 2024

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   In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of learning a solution operator for different computational domains is a problem of general importance for a variety of engineering applications. To this end, we propose a physics-informed deep operator network (DeepONet) capable of predicting the scattered pressure field for arbitrarily shaped scatterers using a geometric parameterization approach based on non-uniform rational B-splines (NURBS). This approach also results in parsimonious representations of non-trivial scatterer geometries. In contrast to existing physics-based approaches that require model re-evaluation when changing the computational domains, our trained model is capable of learning solution operator that can approximate physically-consistent scattered pressure field in just a few seconds for arbitrary rigid scatterer shapes; it follows that the computational time for forward simulations can improve (i.e. be reduced) by orders of magnitude in comparison to the traditional forward solvers. In addition, this approach can evaluate the scattered pressure field without the need for labeled training data. After presenting the theoretical approach, a comprehensive numerical study is also provided to illustrate the remarkable ability of this approach to simulate the acoustic pressure fields resulting from arbitrary combinations of arbitrary scatterer geometries. These results highlight the unique generalization capability of the proposed operator learning approach.

   @article{nair2024physics,
     title = {Physics and geometry informed neural operator network with application to acoustic scattering},
     author = {Nair, Siddharth and Walsh, Timothy F and Pickrell, Greg and Semperlotti, Fabio},
     journal = {arXiv preprint arXiv:2406.03407},
     year = {2024},
   }

5. Springer-EC

   Multiple scattering simulation via physics-informed neural networks

   Siddharth Nair ,  Timothy F Walsh ,  Greg Pickrell ,  and  Fabio Semperlotti

   Engineering with Computers, 2024

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   This work presents a physics-driven machine learning framework for the simulation of acoustic scattering problems. The proposed framework relies on a physics-informed neural network (PINN) architecture that leverages prior knowledge based on the physics of the scattering problem as well as a tailored network structure that embodies the concept of the superposition principle of linear wave interaction. The framework can also simulate the scattered field due to rigid scatterers having arbitrary shape as well as high-frequency problems. Unlike conventional data-driven neural networks, the PINN is trained by directly enforcing the governing equations describing the underlying physics, hence without relying on any labeled training dataset. Remarkably, the network model has significantly lower discretization dependence and offers simulation capabilities akin to parallel computation. This feature is particularly beneficial to address computational challenges typically associated with conventional mesh-dependent simulation methods. The performance of the network is investigated via a comprehensive numerical study that explores different application scenarios based on acoustic scattering.

   @article{nair2024multiple,
     title = {Multiple scattering simulation via physics-informed neural networks},
     author = {Nair, Siddharth and Walsh, Timothy F and Pickrell, Greg and Semperlotti, Fabio},
     journal = {Engineering with Computers},
     pages = {1--20},
     year = {2024},
     publisher = {Springer},
   }

2023

1. SPIE-2023

   A deep learning approach for the inverse shape design of 2D acoustic scatterers

   Siddharth Nair ,  Timothy F Walsh ,  Gregory Pickrell ,  and  Fabio Semperlotti

   In Health Monitoring of Structural and Biological Systems XVII , 2023

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   In this study, we develop an end-to-end deep learning-based inverse design approach to determine the scatterer shape necessary to achieve a target acoustic field. This approach integrates non-uniform rational B-spline (NURBS) into a convolutional autoencoder (CAE) architecture while concurrently leveraging (in a weak sense) the governing physics of the acoustic problem. By utilizing prior physical knowledge and NURBS parameterization to regularize the ill-posed inverse problem, this method does not require enforcing any geometric constraint on the inverse design space, hence allowing the determination of scatterers with potentially any arbitrary shape (within the set allowed by NURBS). A numerical study is presented to showcase the ability of this approach to identify physically-consistent scatterer shapes capable of producing user-defined acoustic fields.

   @inproceedings{nair2023deep,
     title = {A deep learning approach for the inverse shape design of 2D acoustic scatterers},
     author = {Nair, Siddharth and Walsh, Timothy F and Pickrell, Gregory and Semperlotti, Fabio},
     booktitle = {Health Monitoring of Structural and Biological Systems XVII},
     volume = {12488},
     pages = {256--264},
     year = {2023},
     organization = {SPIE},
   }

2. Elsevier-CMAME

   GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning

   Siddharth Nair ,  Timothy F Walsh ,  Greg Pickrell ,  and  Fabio Semperlotti

   Computer Methods in Applied Mechanics and Engineering, 2023

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   This study presents a deep learning based methodology for both remote sensing and design of acoustic scatterers. The ability to determine the shape of a scatterer, either in the context of material design or sensing, plays a critical role in many practical engineering problems. This class of inverse problems is extremely challenging due to their high-dimensional, nonlinear, and ill-posed nature. To overcome these technical hurdles, we introduce a geometric regularization approach for deep neural networks (DNN) based on non-uniform rational B-splines (NURBS) and capable of predicting complex 2D scatterer geometries in a parsimonious dimensional representation. Then, this geometric regularization is combined with physics-embedded learning and integrated within a robust convolutional autoencoder (CAE) architecture to accurately predict the shape of 2D scatterers in the context of identification and inverse design problems. An extensive numerical study is presented in order to showcase the remarkable ability of this approach to handle complex scatterer geometries while generating physically-consistent acoustic fields. The study also assesses and contrasts the role played by the (weakly) embedded physics in the convergence of the DNN predictions to a physically consistent inverse design.

   @article{nair2023grids,
     title = {GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning},
     author = {Nair, Siddharth and Walsh, Timothy F and Pickrell, Greg and Semperlotti, Fabio},
     journal = {Computer Methods in Applied Mechanics and Engineering},
     volume = {414},
     pages = {116167},
     year = {2023},
     publisher = {Elsevier},
   }

2022

1. Elsevier-MSSP

   Nonlocal acoustic black hole metastructures: Achieving broadband and low frequency passive vibration attenuation

   Siddharth Nair ,  Mehdi Jokar ,  and  Fabio Semperlotti

   Mechanical Systems and Signal Processing, 2022

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   This paper introduces the concept of nonlocal Acoustic Black Hole (ABH) metastructure and explores, via numerical analyzes, the corresponding vibration attenuation performance. Building on the basic concept of ABH metastructure, which is a thin plate waveguide with embedded periodic grids of ABHs, this work explores the feasibility of using intentionally introduced nonlocality to expand the dynamic operating range of the ABH absorbers. The nonlocal design is expressively conceived to address the two-fold objective of lowering the cut-on frequency of an individual ABH and extending the operating frequency range towards the lower part of the frequency spectrum (or, equivalently, towards longer wavelengths). The role of nonlocality on the transient and steady state dynamic response of the periodic metastructure is investigated via a dedicated semi-analytical model. Different nonlocal designs are presented and their dynamic performances are investigated and compared using numerical models. Results show a remarkable ability of the nonlocal metastructure to achieve significant vibration attenuation behavior in the low frequency bandwidth.

   @article{nair2022nonlocal,
     title = {Nonlocal acoustic black hole metastructures: Achieving broadband and low frequency passive vibration attenuation},
     author = {Nair, Siddharth and Jokar, Mehdi and Semperlotti, Fabio},
     journal = {Mechanical Systems and Signal Processing},
     volume = {169},
     pages = {108716},
     year = {2022},
     publisher = {Elsevier},
   }

2021

1. JASA

   Broadband vibration attenuation via nonlocal acoustic black hole metastructures

   Siddharth Nair ,  Mehdi Jokar ,  and  Fabio Semperlotti

   The Journal of the Acoustical Society of America, 2021

   Bib HTML

   @article{nair2021broadband,
     title = {Broadband vibration attenuation via nonlocal acoustic black hole metastructures},
     author = {Nair, Siddharth and Jokar, Mehdi and Semperlotti, Fabio},
     journal = {The Journal of the Acoustical Society of America},
     volume = {150},
     number = {4},
     pages = {A342--A342},
     year = {2021},
     publisher = {Acoustical Society of America},
   }

2019

1. MS Thesis

   Nonlocal acoustic black hole metastructures: Achieving ultralow frequency and broadband vibration attenuation

   Siddharth Nair

   Purdue University , 2019

   Bib HTML

   @phdthesis{nair2019nonlocal,
     title = {Nonlocal acoustic black hole metastructures: Achieving ultralow frequency and broadband vibration attenuation},
     author = {Nair, Siddharth},
     year = {2019},
     school = {Purdue University},
   }