Inverse Design

Inverse materials design is shifting materials discovery from forward prediction to targeted proposal of candidates that satisfy objectives under physical constraints. Here, we review recent advances in generative crystal structure modeling, multimodal learning, and closed-loop design pipelines for crystalline solids. We survey how modern generators learn chemical-structural priors from large databases to enable controllable sampling of periodic structures, and compare leading model classes including variational autoencoders, normalizing flows, autoregressive formulations, and diffusion models. Particular attention is given to how feasibility constraints and physical priors are enforced across the workflow, through representation choices, training objectives, sampling-time guidance, and post-generation screening and relaxation. We also discuss how multimodal learning fuses diverse materials modalities, including crystal structures, thermodynamic, electronic information, microscopy, spectroscopy, processing context, and scientific text, to construct a more universal, transferable representation of chemical space. In addition, diverse inverse-design strategies are examined, particularly those that integrate conditional generation with latent optimization, Bayesian optimization, reinforcement learning, and active learning. Finally, we highlight recurring failure modes, such as surrogate exploitation, diversity collapse, distribution shift, and the stability-synthesizability gap, and outline discovery-grade evaluation practices based on staged reporting of validity, novelty, uniqueness, stability, and cost.

In semiconductor manufacturing, lithography projects circuit layouts onto silicon wafers through an optical mask. As circuit features shrink below the wavelength of light, optical diffraction causes the printed patterns to deviate from their intended layouts. Inverse Lithography Technology (ILT) addresses this challenge by generating optimized masks that enhance the fidelity of pattern transfer onto wafers. While ILT resembles an image synthesis task, its reliance on explicit physical metrics for mask evaluation limits the applicability of existing generative models. We introduce LithoGRPO, an ILT framework that integrates the flow-matching paradigm with GRPO-based reinforcement learning (RL) fine-tuning, enabling efficient exploration of diverse masks for a given target layout. Unlike purely generative or optimization-based approaches, RL in LithoGRPO exploits the explicitly defined, physics-based reward function of ILT, enabling optimization under complex, process-aware constraints. To the best of our knowledge, this is the first framework that unifies flow matching and RL for mask optimization. To improve RL sampling efficiency, we propose a fast shot-counting algorithm for manufacturability evaluation, achieving over 130x speedup while preserving the mask ranking of the traditional shot-count metric. Extensive experiments demonstrate that LithoGRPO achieves state-of-the-art performance over both optimization-based and learning-based methods, while maintaining efficient mask generation.

Photonic crystal fiber (PCF) inverse design remains challenging because candidate geometries must satisfy coupled optical targets under expensive electromagnetic simulation. Existing pipelines improve surrogate prediction or one-shot parameter recommendation, but they do not accumulate reusable design knowledge across iterative trials. We formulate PCF inverse design as a memory-policy learning problem and propose SkillPCF, a closed-loop agent framework that combines a physics-guided memory skill bank, reinforcement-learned skill selection, and simulator-grounded skill evolution. We further construct a real-world dataset with 479 expert interaction traces (2,507 spans) and 553 memory-dependent evaluation queries covering dispersion engineering, loss optimization, and multi-objective design. Experiments across multiple LLM backbones and classical baselines show that SkillPCF achieves stronger design-quality and efficiency trade-offs under practical simulation budgets, demonstrating the effectiveness of our proposed memory-skill learning paradigm for physics-aware PCF inverse design.

A novel two-phase molecule inference framework, mol-infer, has recently been developed to infer chemical graphs with prescribed abstract structures and desired property values through mixed integer linear programming (MILP) under the two-layered model, with guaranteed optimality and exactness relative to the given learned prediction function and structural constraints. In this study, we extend this framework to copolymers by introducing a simple feature representation, called the mixing vector (MV) model. In the proposed model, a copolymer feature vector is represented as a convex combination of MILP-tractable monomer descriptors weighted by the mixing ratio of the constituent monomers. This representation does not require explicit sequence-class information and is therefore naturally compatible with MILP-based inverse design. Under this model, we construct prediction functions for several copolymer property datasets using artificial neural networks, reduced quadratic multiple linear regression, and random forests. The proposed representation achieves practically useful predictive performance across multiple physicochemical property datasets; in particular, the best test R^2 score exceeds 0.7 for nine of the ten datasets and exceeds 0.9 for six datasets. We also formulate a multi-monomer inverse-design problem under the MV representation with a prescribed mixing ratio and show that the resulting MILP instances remain tractable, even for three-monomer settings. Finally, we perform an external consistency check by re-evaluating the inferred candidates and comparing the re-computed property values with those predicted by the learned model. Overall, the proposed framework gives a tractable first step toward model-level exact inverse design of copolymers under the two-layered model.

Inverse design of materials has significantly advanced target-driven formulation optimization, yet existing materials machine learning benchmarks remain limited to forward property prediction, failing to systematically evaluate inverse optimization and generation algorithms, a critical gap that hinders the progress of target-driven materials design. To address this limitation, we propose MatFormBench, a novel benchmarking ecosystem tailored to evaluate and guide generative strategies for target-driven formulation. MatFormBench integrates a physics-driven formulation generation scheme to generate synthetic samples that faithfully emulate realistic materials structure-property response relationships, complemented by five escalating difficulty levels to quantify the complexity of these relationships. To rigorously assess algorithm performance, we further propose MatFormScore, a multi-dimensional metric that comprehensively quantifies performance across five critical axes: target success, search efficiency, exploratory capacity, robustness, and stability. We validate MatFormBench by evaluating 39 diverse inverse design algorithms, covering classical surrogate-assisted black-box search, state-of-the-art deep generative models, and increasingly popular Large Language Model (LLM)-based recommendation strategies. Across 1170 standardized algorithm-task evaluations, diffusion-based models demonstrate the strongest overall performance, while Variational Autoencoder (VAE)-based and Genetic Algorithm (GA)-based methods exhibit distinct advantages in specific scenarios. By establishing a unified evaluation standard for target-driven materials formulation, MatFormBench enables reproducible benchmarking, principled algorithm comparison, and diagnostic analysis of inverse design strategies, providing a foundational tool for advancing materials inverse design.

Polymer discovery is central to fields ranging from energy storage to biomedicine, but it is hindered by an astronomically large chemical design space and fragmented representations of structure, properties, and prior knowledge. This fragmentation leaves many AI models disconnected from physical and experimental reality, restricting their ability to support directly actionable design decisions. Here we introduce PolyFusionAgent, an interactive framework coupling a multimodal polymer foundation model (PolyFusion) with a tool-augmented, literature-grounded design agent (PolyAgent). PolyFusion aligns complementary polymer views including sequence, topology, 3D geometry, and fingerprints across millions of polymers to learn a shared latent space transferable across chemistries and data regimes, improving thermophysical property prediction and enabling property-conditioned generation of chemically valid, structurally novel polymers beyond the reference design space. PolyAgent closes the design loop by linking prediction and inverse design with evidence retrieval from the polymer literature, proposing, evaluating, and contextualizing hypotheses with explicit precedent in one workflow. Together, PolyFusionAgent enables interactive, evidence-linked polymer discovery combining large-scale representation learning, multimodal chemical knowledge, and verifiable scientific reasoning.

The inverse problem of multilayer thin-film optical coatings design represents a complex combinatorial-continuous optimization challenge. We present PRISM (Position-encoded Regressive Inverse Spectral Model), a unified decoder-only autoregressive transformer that streamlines this process by jointly predicting discrete material selection and continuous thickness regression within a single backbone. PRISM introduces two primary architectural innovations: (1) spectrum prefix conditioning, which utilizes standard prefix tokens for in-context target injection, and (2) cumulative-depth Rotary Position Embeddings, which encode continuous thickness directly into the positional representation to preserve the physical spatial relationships of the stack. Our benchmarks demonstrate that a PRISM-13M model reduces MAE by over 50% compared to other transformer baselines while utilizing only one-fifth of the parameters. Furthermore, a 44M-parameter variant achieves state-of-the-art performance (MAE = 0.010) on our in-distribution validation benchmark and operates significantly faster than simulated annealing, offering a highly efficient alternative to classical optimization methods.

Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited by the cost of repeated high-fidelity simulations required for gradient-based Markov chain Monte Carlo (MCMC) sampling. While surrogate models are commonly proposed to reduce this cost, their effect on posterior geometry and uncertainty, especially for shock-dominated flows, remains poorly understood. In this work, we demonstrate that neural operator surrogates can be embedded directly within the MCMC inference loop while preserving posterior structure. Using a fully Bayesian inverse formulation of quasi-one-dimensional nozzle flow, we demonstrate that geometry parameterization plays a decisive role in identifiability and posterior conditioning, with cubic B-splines yielding stable and physically meaningful uncertainty estimates. Building on this formulation, a Deep Operator Network trained on CFD-generated data is substituted for the CFD solver within a No-U-Turn Sampler, while keeping the likelihood model, priors, and sampling configuration unchanged. Across sparse to fully observed regimes, surrogate-based inference reproduces the posterior geometry and uncertainty trends of the CFD reference. As a result of surrogate integration, total inference time is reduced to under one second, corresponding to a speedup exceeding three orders of magnitude. In addition, a direct inverse neural operator is examined as a deterministic alternative for inverse design, enabling single-shot geometry reconstruction without posterior sampling. These results demonstrate that neural operator-accelerated Bayesian inference enables practical, uncertainty-aware inverse design workflows for aerodynamic applications.

Inverse design of metasurfaces under continuous electromagnetic constraints requires generation of geometries that simultaneously satisfy stringent spectral specifications and remain manufacturable. Conventional approaches based on iterative full wave simulations are computationally prohibitive for large design spaces, while existing generative models often suffer from poor conditional controllability and limited fabrication awareness. In this regard, we propose a physics guided condition quality enhanced diffusion framework for the inverse design of metasurface based absorbers. Fabrication-aware constraints are incorporated to ensure practical realizability of the generated designs. The framework introduces a conditioning mechanism for continuous spectral specifications, wherein feature-wise linear modulation propagates the condition across the denoising hierarchy, enabling stable and accurate generation with improved spectral controllability. Further, to embed EM consistency directly into the generative learning process, a pre trained surrogate EM simulator is integrated within the diffusion training pipeline. The proposed framework generated physically realizable metasurface designs for diverse reflection characteristics in the frequency range of 2 to 18 GHz, achieving a very low average spectral mean squared error of 0.0006 and a high band alignment accuracy of 0.958. The framework also addresses the fundamentally non-unique nature of inverse EM design by enabling structured multimodal generation of geometrically distinct yet spectrally consistent metasurface designs for the same target response. The proposed model produces the suitable design in approximately 30 seconds, whereas the conventional approach can take several months under comparable computational resources. The efficiency of the model is also established via experimental measurements.

Property prediction and inverse structural design of catalytic materials are typically modeled as two independent tasks: the former predicts target properties from given structures, whereas the latter generates candidate structures according to desired properties. Although the decoupled paradigm facilitates the implementation of a generation--evaluation--screening'' workflow, the inconsistency between the generative model and the property prediction model in terms of representation spaces and training objectives can readily introduce data distribution shifts and evaluator bias, thereby limiting the stability of closed-loop optimization. In this work, we propose CatalyticMLLM, a unified graph--text multimodal large language model for catalytic materials, which integrates property prediction and **inverse design** within the same model and shared representation space. Under this unified framework, CatalyticMLLM can not only perform reliable property prediction by leveraging three-dimensional structures and textual information, but also generate and screen physically feasible CIF candidates conditioned on target properties, thereby forming a closed-loop optimization workflow of inverse design--prediction--screening--redesign.'' Experimental results demonstrate that this unified paradigm outperforms decoupled baselines on both catalytic relaxed-energy prediction and inverse design tasks, validating the effectiveness of jointly modeling property prediction and structure generation within a single multimodal model.

Solving inverse partial differential equation (PDE) problems is a fundamental topic in scientific research due to its broad significance across a wide range of real-world applications. Inverse PDE problems arise across medical imaging, geophysics, materials science, and aerodynamics, where the goal is to infer hidden causes, design structures, or control physical states. In this paper, we provide a comprehensive review of recent advances in solving inverse PDE problems using artificial intelligence (AI). We first introduce the basic formulation, key challenges, and traditional numerical foundations of inverse PDE problems, and then organize it into three major categories: inverse problems, inverse design, and control problems. For each category, we further present a methodological paradigms, and review representative state-of-the-art approaches from recent years. We then summarize representative applications across scientific and industrial domains, including mechanical systems, aerodynamic problems, thermal systems, full-waveform inversion, system identification, and medical imaging. Finally, we discuss open challenges and future prospects, such as physics-informed architectures, limited real-world data, uncertainty quantification, and inverse foundation models. This survey aims to provide the first unified and systematic perspective on AI for inverse PDE problems, demonstrating how modern learning-based methods are reshaping inverse problems, inverse design, and control problems in PDE-governed systems.

Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling inherent to classical Archard and Greenwood-Williamson models, severely restricting their functional range. Here, we propose a framework for the inverse design of tribological metainterfaces engineered for programmable contact behaviors. By utilizing general axisymmetric asperities, we unlock nonlinear macroscopic responses unattainable by standard Hertzian contacts. To solve the inverse problem, we embed a fully differentiable contact mechanics engine within a neural network and a quadratic optimizer. We leverage regularized physical gradients to automatically discover non-standard topographies that reproduce complex target friction laws, with only a few asperities in unit cells. The predicted designs are strictly validated against high-fidelity Boundary Element Method (BEM) simulations. This framework bridges data-driven optimization and rigorous physics, offering a scale-invariant pathway for discovering functional tribological surfaces.

Generative models are powerful tools for sampling from a learned distribution $\mathcal{P}(Y \mid X)$, and inverse-design methods invert this map to find an input $x$ that produces a desired point output $y^*$. However, many design goals are naturally distributional rather than pointwise, incorporating the inherent uncertainty of $Y$ and targeting a specific form for it, a task not addressed by standard inverse design. To address this issue we introduce Conditional Distribution Matching (CDM), a new inverse-design problem class in generative modeling: given a joint distribution $\mathcal{P}(X, Y)$ and a target distribution $\mathcal{G}(Y)$, find an input $x^*$ whose induced conditional distribution $\mathcal{P}(Y \mid X = x^*)$ matches $\mathcal{G}$. We formally define two variants: Conditional Distribution Matching Sampling (CDMS) and Conditional Distribution Matching Optimization (CDMO). To solve these problems, we propose MLGD-F (Matching-Loss Guided Diffusion with a Fast inner sampler), a plug-and-play inference-time algorithm that combines a pretrained score-based diffusion model with a pretrained fast conditional sampler, requiring no additional training or fine-tuning. By leveraging single-step conditional sampling, MLGD-F enables tractable gradient computation, making the estimation of $\mathcal{P}(Y \mid X)$ both memory-efficient and computationally lightweight. We validate MLGD-F on synthetic benchmarks, structured image transformations, and generative editing optimization, demonstrating reliable recovery of inputs whose conditional distributions match diverse user-specified targets, including discrete mixtures and continuous low-rank supports.

Inverse design of RF passive components from S-parameters is a high-dimensional, ill-posed problem, and prior generative approaches are limited to single-layer binary-metallization structures. This paper presents an inverse design approach that generates passive components from partial S-parameter inputs on an $8\times8$ mm board discretized at $64\times64$ pixels with sub-pixel grayscale metallization across 1-20 GHz. The framework generates two-layer copper layouts with vias, with hard physical constraints on feed locations enforced through annealed Langevin projection, flexible multi-modal conditioning on partial S-parameter specifications, port locations, dielectric properties, reference topology, and variable port placement. Candidate designs are generated in seconds, with surrogate-predicted S-parameters matching targets to within $0.77 \pm 1.28$ dB weighted mean absolute error. We validate the approach with two fabricated designs on RO4003C: a manufacturable alternative to a hairpin filter whose coupling gaps violate fabrication rules, and a combline bandpass filter designed from scratch given only target S-parameters.

Amorphous (disordered) materials are solids that have shown great potential in various domains, including energy storage, thermal management, and advanced materials. Unlike crystalline materials that can be described by unit cells containing a few to hundreds of atoms, amorphous materials require larger simulation cells with at least hundreds to thousands of atoms. To advance the design of amorphous materials with desired properties and facilitate the exploration of their vast design space, generative inverse design has emerged as a promising approach. It aims to directly output materials with properties closely aligned with the desired ones using probabilistic generative models conditioned on desired properties, which can be more resource efficient than the traditional trial-and-error approach. However, due to the inherent stochasticity of probabilistic generative models, when element assignments are unconstrained, a large portion of generated materials may be charge unbalanced, and no existing methods can effectively mitigate this limitation. In this work, we propose AMGenC, a new generative inverse design method for amorphous materials that can guarantee the generation of charge balanced samples, with minimal additional computational overhead and without sacrificing inverse design accuracy. AMGenC achieves this through an element noise that gives the generation process a starting point centered around charge balance, and the combination of a per-step soft projection and a final discrete projection for steering the elements toward exact charge balance throughout the generation. We perform extensive experiments on two amorphous materials datasets. Experimental results provide evidence that AMGenC achieves its design goal.

Metamaterial discovery seeks microstructured materials whose geometry induces targeted mechanical behavior. Existing inverse-design methods can efficiently generate candidates, but they typically require explicit numerical property targets and are less suitable for early-stage exploration, where researchers often begin with incomplete constraints and qualitative intents expressed in natural language. Large language models can interpret such intents, but they lack geometric awareness and physical property validity. To address this gap, we propose MetaSymbO, a multi-agent framework for language-guided Metamaterial discovery via Symbolic-driven latent evOlution. Specifically, MetaSymbO contains three agents: a Designer that interprets free-form design intents and retrieves a semantically consistent scaffold, a Generator that synthesizes candidate microstructures in a disentangled latent space, and a Supervisor that provides fast property-aware feedback for iterative refinement. To move beyond the limitations of reproducing known samples from literature and training data, we further introduce symbolic-driven latent evolution, which applies programmable operators over disentangled latent factors to compose, modify, and refine structures at inference time. Extensive experiments demonstrate that (i) MetaSymbO improves structural validity by up to 34% in symmetry and nearly 98% in periodicity compared to state-of-the-art baselines; (ii) MetaSymbO achieves about 6-7% higher language-guidance scores while maintaining superior structure novelty compared to advanced reasoning LLMs; (iii) qualitative analyses confirm the effectiveness of symbolic logic operators in enabling programmable semantic alignment; and (iv) realworld case studies on auxetic, high-stiffness metamaterial design further validate its practical capability.

The need to burn 100% H2 in high efficient gas turbines featuring low NOx combustion in premix mode require the complete redesign of the combustion system to ensure stable operation without any flashback. Since all engine frames featuring a power range from 4 MW up to 600 MW are affected, a huge design effort is expected. To reduce this effort, especially to transfer knowledge between the different engine classes, generative design methods using latest AI technology will provide promising potential. In this work, this challenge is approached utilizing the current advances in generative artificial intelligence. We train an Invertible Neural Network (INN) on an expandable database of geometrically parameterized combustor designs with simulated performance labels. Utilizing the INN in its inverse direction, multiple design proposals are generated which fulfill specified performance labels.

AI is increasingly used to accelerate engineering design by improving decision-making and shortening iteration cycles. Application to marine propeller design, however, remains challenging due to scarce training data and the lack of widely available pretrained models. We address this gap with a physics-based data generation pipeline and a generative-AI framework for direct performance-to-design generation tailored to marine propellers. First, we build a database of over 20,000 four- and five-bladed propeller geometries, each accompanied by simulated open-water performance curves. On top of this dataset, we develop a three-module design framework: (1) A Conditional Generation Model that proposes candidate geometries conditioned on design specifications such as target thrust, power, and diameter. (2) A Performance Prediction Model, implemented as a neural-network surrogate, that predicts thrust, torque, and efficiency in milliseconds, enabling rapid evaluation of generated designs. (3) A design refinement stage that applies evolutionary optimization to enforce practical constraints such as required thrust under power limits and bounds on blade-area ratio and thickness. Experimental results over a range of operating conditions show that the framework can generate hydrodynamically plausible propeller designs that match prescribed performance targets while substantially reducing design-iteration time relative to the traditional expert-guided refinement. Latent diffusion-based generator produces more diverse designs under the same conditions than the conditional variational autoencoder, suggesting a stronger capacity for design-space exploration with diffusion models. By coupling physics-based data synthesis with modular AI models, the proposed approach streamlines the propeller design cycle and reduces reliance on expensive high-fidelity simulations to final validation stages.

Meta-optics promises compact, high-performance imaging and color routing. However, designing high-performance structures is a high-dimensional optimization problem: mapping a desired optical output back to a physical 3D structure requires solving computationally expensive Maxwell's equations iteratively. Even with adjoint optimization, broadband design can require thousands of Maxwell solves, making industrial-scale optimization slow and costly. To overcome this challenge, we propose the Neural Adjoint Method, a solver-supervised surrogate that predicts 3D adjoint gradient fields from a voxelized permittivity volume using a Fourier Neural Operator (FNO). By learning the dense, per-voxel sensitivity field that drives gradient-based updates, our method can replace per-iteration adjoint solves with fast predictions, greatly reducing the computational cost of full-wave simulations required during iterative refinement. To better preserve sensitivity peaks, we introduce a stage-wise FNO that progressively refines residual errors with increasing emphasis on higher-frequency components. We curate a meta-optics dataset from paired forward/adjoint FDTD simulations and evaluate it across three tasks: spectral sorting (color routers), achromatic focusing (metalenses), and waveguide mode conversion. Our method reduces design time from hours to seconds. These results suggest a practical route toward fast, large-scale volumetric meta-optical design enabled by AI-accelerated scientific computing.

Kirigami is an increasingly useful fabrication method to produce shape-programmable metamaterial structures. However, inverse design remains difficult because deployment is nonlinear, and feasible cut layouts must satisfy discrete compatibility rules, avoid overlap, and map one target shape to valid designs. We present RL-Kirigami, an inverse design framework that combines optimal-transport conditional flow matching (OT-CFM) with reinforcement learning to generate compatible ratio fields for compact reconfigurable parallelogram quad kirigami. A marching decoder enforces global geometric compatibility, and Group Relative Policy Optimization (GRPO) aligns the generator with nondifferentiable rewards for silhouette matching, feasibility, and ratio-field regularity. Across procedurally generated target shape instances, a single sample from the pretrained OT-CFM prior reached $94.2\%~\mathrm{sIoU}$ and outperformed solver baselines while reducing forward simulator evaluations from hundreds to $1$. GRPO improved accuracy to $94.91\%~\mathrm{sIoU}$ and, with regularity included, reduced $\mathrm{TV}(\mathbf{x})$ from $0.95$ to $0.81$ while maintaining $94.83\%~\mathrm{sIoU}$. Generated layouts were exported to DXF and laser cut in $50~μ\mathrm{m}$ polymeric sheets to produce deployable prototypes in $8.0\pm 1.0$ minutes per part. These results support a manufacturing-aware inverse design workflow for deployable kirigami metamaterials under geometric feasibility constraints. Code is available at https://github.com/milad1378yz/RL-Kirigami.

Urban areas are increasingly vulnerable to thermal extremes driven by rapid urbanization and climate change. Traditionally, thermal extremes have been monitored using Earth-observing satellites and numerical modeling frameworks. For example, land surface temperature derived from Landsat or Sentinel imagery is commonly used to characterize surface heating patterns. These approaches operate as forward models, translating radiative observations or modeled boundary conditions into estimates of surface thermal states. While forward models can predict land surface temperature from vegetation and urban form, the inverse problem of determining spatial vegetation configurations that achieve a desired regional temperature shift remains largely unexplored. This task is inherently underdetermined, as multiple spatial vegetation patterns can yield similar aggregated temperature responses. Conventional regression and deterministic neural networks fail to capture this ambiguity and often produce averaged solutions, particularly under data-scarce conditions. We propose a conflated inverse modeling framework that combines a predictive forward model with a diffusion-based generative inverse model to produce diverse, physically plausible image-based vegetation patterns conditioned on specific temperature goals. Our framework maintains control over thermal outcomes while enabling diverse spatial vegetation configurations, even when such combinations are absent from training data. Altogether, this work introduces a controllable inverse modeling approach for urban climate adaptation that accounts for the inherent diversity of the problem. Code is available at the GitHub repository.

Conventional microwave engineering education relies heavily on analytical methods, canonical circuit topologies, and intuition-driven design, which have proven effective at microwave frequencies. However, as systems increasingly operate in the millimeter-wave and terahertz regimes, parasitic effects, process-dependent electromagnetic interactions, and ultra-wideband performance requirements challenge both topology/layout-constrained traditional design methodologies and existing teaching paradigms. This paper proposes a pedagogical shift in microwave and RFIC (Radio Frequency Integrated Circuit) engineering and education by introducing machine-learning (ML) and data-driven electromagnetic synthesis as a complementary design framework for microwave circuits such as power dividers and combiners, couplers, and baluns. Rather than emphasizing predefined topologies, the proposed approach enables topology-agnostic, performance-oriented exploration of the design space, allowing students to directly engage with electromagnetic behavior through specification-driven synthesis. By integrating machine-learning-based inverse design and multi-objective optimization into the curriculum, the framework enhances physical intuition, encourages design creativity, and better aligns microwave education with emerging industrial practices in high-frequency and ultra-wideband system design.

Machine learning is revolutionizing chemistry. Beyond the value of predictive models accelerating virtual screening, generative AI aims at enabling inverse design, reversing the compound-to-property prediction paradigm into property-to-compound generation. Chemists now have access to a rich AI toolbox for organic chemistry, including drug discovery. However, the application of these methods to inorganic compounds remains limited by the challenges posed by their intrinsic nature. This Review analyzes how these challenges have been addressed, considering widely diverse systems ranging from molecules to crystals, including transition metal complexes and microporous materials. The analysis focuses on how generative AI methods have evolved towards data-representation-model pipelines that address the full complexity of inorganic compounds, including their chemical composition, geometry, symmetry, and electronic structure. Future directions, like benchmark standardization and the development of synthesizability metrics, are also discussed.

A fundamental obstacle to causal discovery from text is the lack of causally annotated text data for use as ground truth, due to high annotation costs. This motivates an important task of generating text with causal graph annotations. Early template-based generation methods sacrifice text naturalness in exchange for high causal graph annotation accuracy. Recent Large Language Model (LLM)-dependent methods directly generate natural text from target graphs through LLMs, but do not guarantee causal graph annotation accuracy. Therefore, we propose iTAG, which performs real-world concept assignment to nodes before converting causal graphs into text in existing LLM-dependent methods. iTAG frames this process as an inverse problem with the causal graph as the target, iteratively examining and refining concept selection through Chain-of-Thought (CoT) reasoning so that the induced relations between concepts are as consistent as possible with the target causal relationships described by the causal graph. iTAG demonstrates both extremely high annotation accuracy and naturalness across extensive tests, and the results of testing text-based causal discovery algorithms with the generated data show high statistical correlation with real-world data. This suggests that iTAG-generated data can serve as a practical surrogate for scalable benchmarking of text-based causal discovery algorithms.

Epithelial tissues dynamically reshape through local mechanical interactions among cells, a process well captured by vertex models. Yet their many tunable parameters make inference and optimization challenging, motivating computational frameworks that flexibly model and learn tissue mechanics. We introduce VertAX, a differentiable JAX-based framework for vertex-modeling of confluent epithelia. VertAX provides automatic differentiation, GPU acceleration, and end-to-end bilevel optimization for forward simulation, parameter inference, and inverse mechanical design. Users can define arbitrary energy and cost functions in pure Python, enabling seamless integration with machine-learning pipelines. We demonstrate VertAX on three representative tasks: (i) forward modeling of tissue morphogenesis, (ii) mechanical parameter inference, and (iii) inverse design of tissue-scale behaviors. We benchmark three differentiation strategies-automatic differentiation, implicit differentiation, and equilibrium propagation-showing that the latter can approximate gradients using repeated forward, adjoint-free simulations alone, offering a simple route for extending inverse biophysical problems to non-differentiable simulators with limited additional engineering effort.

We address the inverse problem of designing two-dimensional reflectors that transform light from a finite, extended source into a prescribed far-field distribution. The reflector height is represented by a neural network and optimized with two objective functions: a direct change-of-variables loss based on the closed-form inverse ray map, and a mesh-based loss that maps target cells back to the source and remains usable for discontinuous sources. Gradients are computed by automatic differentiation and minimized with a robust quasi-Newton method. As a baseline, we adapt a deconvolution pipeline built on a simplified finite-source approximation: a one-dimensional monotone map is recovered from flux balance, converted to a reflector by an integrating-factor ODE solve, and embedded in a modified Van Cittert iteration with nonnegativity clipping and ray-traced feedback. Across four benchmarks, covering continuous and discontinuous sources and minimum-height constraints, accuracy is measured by ray-traced normalized mean absolute error. On the two main benchmarks, the neural method reaches errors of about 2e-5 and 5e-5 within a few seconds on one NVIDIA RTX 4090 GPU, compared with 4e-3 and 5e-2 for the deconvolution baseline after several hundred seconds. The results show that the neural formulation is both more accurate and substantially faster, while still supporting practical height constraints. We also discuss extensions to rotationally symmetric and full three-dimensional reflector design through iterative correction schemes.

Metasurface inverse design can realize complex optical functionality, but turning a target optical response into executable optimization code still requires substantial expertise in computational electromagnetics and solver-specific software engineering. We present a self-evolving agentic framework that lowers this barrier by coupling a coding agent, explicit human-readable skill files, and a deterministic physics-based evaluator. Rather than updating model weights, it revises the skill files from solver-grounded feedback, while the base model and differentiable solver, which provides the physics simulation and gradients, stay fixed. On a multi-type benchmark, skill evolution raises same-type task success from 38% to 74%, the fraction of physical criteria met from 0.51 to 0.87, and reduces average attempts from 4.10 to 2.30. On two new-type families, success holds near ceiling on one (0.92 to 0.90) and rises from 0.20 to 0.90 on the other. Skill evolution offers a practical path toward autonomous and accessible inverse-design workflows.

Inverse design of optical multilayer stacks seeks to infer layer materials, thicknesses, and ordering from a desired target spectrum. It is a long-standing challenge due to the large design space and non-unique solutions. We introduce OptoLlama, a masked diffusion language model for inverse thin-film design from optical spectra. Representing multilayer stacks as sequences of material-thickness tokens, OptoLlama conditions generation on reflectance, absorptance, and transmittance spectra and learns a probabilistic mapping from optical response to structure. Evaluated on a representative test set of 3,000 targets, OptoLlama reduces the mean absolute spectral error by 2.9-fold relative to a nearest-neighbor template baseline and by 3.45-fold relative to the state-of-the-art data-driven baseline, called OptoGPT. Case studies on designed and expert-defined targets show that the model reproduces characteristic spectral features and recovers physically meaningful stack motifs, including distributed Bragg reflectors. These results establish diffusion-based sequence modeling as a powerful framework for inverse photonic design.

Amorphous materials are solids that lack long-range atomic order but possess complex short- and medium-range order. Unlike crystalline materials that can be described by unit cells containing few up to hundreds of atoms, amorphous materials require larger simulation cells with at least hundreds or often thousands of atoms. Inverse design of amorphous materials with probabilistic generative models aims to generate the atomic positions and elements of amorphous materials given a set of desired properties. It has emerged as a promising approach for facilitating the application of amorphous materials in domains such as energy storage and thermal management. In this paper, we introduce AMShortcut, an inference- and training-efficient probabilistic generative model for amorphous materials. AMShortcut enables accurate inference of diverse short- and medium-range structures in amorphous materials with only a few sampling steps, mitigating the need for an excessive number of sampling steps that hinders inference efficiency. AMShortcut can be trained once with all relevant properties and perform inference conditioned on arbitrary combinations of desired properties, mitigating the need for training one model for each combination. Experiments on three amorphous materials datasets with diverse structures and properties demonstrate that AMShortcut achieves its design goals.

Designing microstructures with coupled cross-physics objectives is a fundamental challenge where traditional topology optimization is often computationally prohibitive and deep generative models frequently suffer from physical hallucinations. We introduce AutoMS, a multi-agent neuro-symbolic framework that reformulates inverse design as an LLM-driven evolutionary search. AutoMS leverages LLMs as semantic navigators to decompose complex requirements and coordinate agent workflows, while a novel Simulation-Aware Evolutionary Search (SAES) mechanism handles low-level numerical optimization via local gradient approximation and directed parameter updates. This architecture achieves a state-of-the-art 83.8% success rate on 17 diverse cross-physics tasks, significantly outperforming both traditional evolutionary algorithms and existing agentic baselines. By decoupling open-ended semantic orchestration from simulation-grounded numerical search, AutoMS provides a robust pathway for navigating complex physical landscapes that remain intractable for standard generative or purely linguistic approaches.