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1. Inverse Design Framework With Invertible Neural Networks for Passive Vibration Suppression in Phononic Structures

   https://doi.org/10.1115/1.4052300  

   Oddiraju, Manaswin; Behjat, Amir; Nouh, Mostafa; Chowdhury, Souma (February 2022, Journal of Mechanical Design)

   null (Ed.)

   Abstract Automated inverse design methods are critical to the development of metamaterial systems that exhibit special user-demanded properties. While machine learning approaches represent an emerging paradigm in the design of metamaterial structures, the ability to retrieve inverse designs on-demand remains lacking. Such an ability can be useful in accelerating optimization-based inverse design processes. This paper develops an inverse design framework that provides this capability through the novel usage of invertible neural networks (INNs). We exploit an INN architecture that can be trained to perform forward prediction over a set of high-fidelity samples and automatically learns the reverse mapping with guaranteed invertibility. We apply this INN for modeling the frequency response of periodic and aperiodic phononic structures, with the performance demonstrated on vibration suppression of drill pipes. Training and testing samples are generated by employing a transfer matrix method. The INN models provide competitive forward and inverse prediction performance compared to typical deep neural networks (DNNs). These INN models are used to retrieve approximate inverse designs for a queried non-resonant frequency range; the inverse designs are then used to initialize a constrained gradient-based optimization process to find a more accurate inverse design that also minimizes mass. The INN-initialized optimizations are found to be generally superior in terms of the queried property and mass compared to randomly initialized and inverse DNN-initialized optimizations. Particle swarm optimization with INN-derived initial points is then found to provide even better solutions, especially for the higher-dimensional aperiodic structures. 

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2. IKBT: Solving Symbolic Inverse Kinematics with Behavior Tree

   Zhang, Dianmu; Hannaford, Blake (July 2019, Journal of artificial intelligence research and advances)

   Inverse kinematics solves the problem of how to control robot arm joints to achieve desired end effector positions, which is critical to any robot arm design and implemen- tations of control algorithms. It is a common misunderstanding that closed-form inverse kinematics analysis is solved. Popular software and algorithms, such as gradient descent or any multi-variant equations solving algorithm, claims solving inverse kinematics but only on the numerical level. While the numerical inverse kinematics solutions are rela- tively straightforward to obtain, these methods often fail, due to dependency on specific numerical values, even when the inverse kinematics solutions exist. Therefore, closed-form inverse kinematics analysis is superior, but there is no generalized automated algorithm. Up till now, the high-level logical reasoning involved in solving closed-form inverse kine- matics made it hard to automate, so it’s handled by human experts. We developed IKBT, a knowledge-based intelligent system that can mimic human experts’ behaviors in solving closed-from inverse kinematics using Behavior Tree. Knowledge and rules used by engineers when solving closed-from inverse kinematics are encoded as actions in Behavior Tree. The order of applying these rules is governed by higher level composite nodes, which resembles the logical reasoning process of engineers. It is also the first time that the dependency of joint variables, an important issue in inverse kinematics analysis, is automatically tracked in graph form. Besides generating closed-form solutions, IKBT also explains its solving strategies in human (engineers) interpretable form. This is a proof-of-concept of using Behavior Trees to solve high-cognitive problems. 

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3. Phases of dark matter from inverse decays

   https://doi.org/10.1103/987q-fhb6  

   Frumkin, Ronny; Hochberg, Yonit; Kuflik, Eric; Murayama, Hitoshi (August 2025, Physical Review D)

   Inverse decays are an interesting avenue for producing dark matter in the early Universe. We study in detail various phases of dark matter parameter space where inverse decays control its abundance, expanding on our work of inverse decay (INDY) dark matter and going beyond. The role of initial conditions and the impact of departure from kinetic equilibrium are investigated as well. We show how these inverse decay phases can arise in theories of a kinetically mixed dark photon and dark Higgs, with promising prospects for detection at upcoming experiments. 

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4. On the recovery of two function-valued coefficients in the Helmholtz equation for inverse scattering problems via inverse Born series ^*

   https://doi.org/10.1088/1361-6420/ade621  

   Cakoni, Fioralba; Meng, Shixu; Zhou, Zehui (June 2025, Inverse Problems)

   Abstract In this work, we construct the Born and inverse Born approximation and series to recover two function-valued coefficients in the Helmholtz equation for inverse scattering problems from the scattering data at two different wave-numbers. An analysis of the convergence and approximation error of the proposed regularized inverse Born series is provided. The results show that the proposed series converges when the inverse Born approximations of the perturbations are sufficiently small. The preliminary numerical results show the capability of the proposed regularized inverse Born approximation and series for recovering the isotropic inhomogeneous media. 

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5. Generative Adversarial Networks and Mixture Density Networks-Based Inverse Modeling for Microstructural Materials Design

   https://doi.org/10.1007/s40192-022-00285-0  

   Mao, Yuwei; Yang, Zijiang; Jha, Dipendra; Paul, Arindam; Liao, Wei-keng; Choudhary, Alok; Agrawal, Ankit (November 2022, Integrating Materials and Manufacturing Innovation)

   Abstract There are two broad modeling paradigms in scientific applications: forward and inverse. While forward modeling estimates the observations based on known causes, inverse modeling attempts to infer the causes given the observations. Inverse problems are usually more critical as well as difficult in scientific applications as they seek to explore the causes that cannot be directly observed. Inverse problems are used extensively in various scientific fields, such as geophysics, health care and materials science. Exploring the relationships from properties to microstructures is one of the inverse problems in material science. It is challenging to solve the microstructure discovery inverse problem, because it usually needs to learn a one-to-many nonlinear mapping. Given a target property, there are multiple different microstructures that exhibit the target property, and their discovery also requires significant computing time. Further, microstructure discovery becomes even more difficult because the dimension of properties (input) is much lower than that of microstructures (output). In this work, we propose a framework consisting of generative adversarial networks and mixture density networks for inverse modeling of structure–property linkages in materials, i.e., microstructure discovery for a given property. The results demonstrate that compared to baseline methods, the proposed framework can overcome the above-mentioned challenges and discover multiple promising solutions in an efficient manner. 

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