Inverse Design

This article presents a deep learning-driven inverse design methodology for Doherty power amplifiers (PA) with multi-port pixelated output combiner networks. A deep convolutional neural network (CNN) is developed and trained as an electromagnetic (EM) surrogate model to accurately and rapidly predict the S-parameters of pixelated passive networks. By leveraging the CNN-based surrogate model within a blackbox Doherty framework and a genetic algorithm (GA)-based optimizer, we effectively synthesize complex Doherty combiners that enable an extended back-off efficiency range using fully symmetrical devices. As a proof of concept, we designed and fabricated two Doherty PA prototypes incorporating three-port pixelated combiners, implemented with GaN HEMT transistors. In measurements, both prototypes demonstrate a maximum drain efficiency exceeding 74% and deliver an output power surpassing 44.1 dBm at 2.75 GHz. Furthermore, a measured drain efficiency above 52% is maintained at the 9-dB back-off power level for both prototypes at the same frequency. To evaluate linearity and efficiency under realistic signal conditions, both prototypes are tested using a 20-MHz 5G new radio (NR)-like waveform exhibiting a peak-to-average power ratio (PAPR) of 9.0 dB. After applying digital predistortion (DPD), each design achieves an average power added efficiency (PAE) above 51%, while maintaining an adjacent channel leakage ratio (ACLR) better than -60.8 dBc.

Inverse design aims to find design parameters $x$ achieving target performance $y^*$. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow matching (CFM), when adapted to inverse problems by pairing labels with design parameters, exhibits strong sensitivity to their arbitrary ordering and scaling, leading to unstable training. We introduce Diagonal Flow Matching (Diag--CFM), which resolves this through a zero-anchoring strategy that pairs design coordinates with noise and labels with zero, making the learning problem provably invariant to coordinate permutations. This yields substantially lower round-trip error than CFM and invertible neural network baselines across design dimensions up to $P{=}784$, including order-of-magnitude gains on several benchmarks. We develop two architecture-intrinsic uncertainty metrics, Zero-Deviation and Self-Consistency, that enable three practical capabilities: selecting the best candidate among multiple generations, abstaining from unreliable predictions, and detecting out-of-distribution targets; consistently outperforming ensemble and general-purpose alternatives across all tasks. We validate on airfoil, gas turbine combustor, scalable analytical benchmarks, a photonics inverse-design task, and an image-statistics benchmark.

Cold metals are a class of metals with an intrinsic energy gap located close to the Fermi level, which enables cold-carrier injection for steep-slope transistors and is therefore promising for low-power electronic applications. High-throughput screening has revealed 252 three-dimensional (3D) cold metals in the Materials Project database, but database searches are inherently limited to known compounds. Here we present an inverse-design workflow that generates 3D cold metals using MatterGPT, a conditional autoregressive Transformer trained on SLICES, an invertible and symmetry-invariant crystal string representation. We curate a training set of 26,309 metallic structures labeled with energy above hull and a unified band-edge distance descriptor that merges p-type and n-type cold-metal characteristics to address severe label imbalance. Property-conditioned generation targeting thermodynamic stability and 50-500 meV band-edge distances produces 148,506 unique candidates; 92.1% are successfully reconstructed to 3D structures and down-selected by symmetry, uniqueness and novelty filters, followed by high-throughput DFT validation. We identify 257 cold metals verified as novel with respect to the Materials Project database, with gaps around the Fermi level spanning 50-500 meV. First-principles phonon, electronic-structure, and work-function calculations for representative candidates confirm dynamical stability and contact-relevant work functions. Our results demonstrate that SLICES-enabled generative transformers can expand the chemical space of cold metals beyond high-throughput screening, providing a route to low-power electronic materials discovery.

Many of the most important problems in science and engineering are inverse problems: given a desired outcome, find a design that achieves it. Evaluating whether a candidate meets the spec is often routine; a binding energy can be computed, a reactor yield simulated, a pharmacokinetic profile predicted. But searching a combinatorial design space for inputs that satisfy those targets is fundamentally harder. We introduce SciDesignBench, a benchmark of 520 simulator-grounded tasks across 14 scientific domains and five settings spanning single-shot design, short-horizon feedback, long-horizon refinement, and seed-design optimization. On the 10-domain shared-core subset, the best zero-shot model reaches only 29.0% success despite substantially higher parse rates. Simulator feedback helps, but the leaderboard changes with horizon: Sonnet 4.5 is strongest in one-turn de novo design, whereas Opus 4.6 is strongest after 20 turns of simulator-grounded refinement. Providing a starting seed design reshuffles the leaderboard again, demonstrating that constrained modification requires a fundamentally different capability from unconstrained de novo generation. We then introduce RLSF, a simulator-feedback training recipe. An RLSF-tuned 8B model raises single-turn success rates by 8-17 percentage points across three domains. Together, these results position simulator-grounded inverse design as both a benchmark for scientific reasoning and a practical substrate for amortizing expensive test-time compute into model weights.

Today's scientific challenges, from climate modeling to Inertial Confinement Fusion design to novel material design, require exploring huge design spaces. In order to enable high-impact scientific discovery, we need to scale up our ability to test hypotheses, generate results, and learn from them rapidly. We present MADA (Multi-Agent Design Assistant), a Large Language Model (LLM) powered multi-agent framework that coordinates specialized agents for complex design workflows. A Job Management Agent (JMA) launches and manages ensemble simulations on HPC systems, a Geometry Agent (GA) generates meshes, and an Inverse Design Agent (IDA) proposes new designs informed by simulation outcomes. While general purpose, we focus development and validation on Richtmyer--Meshkov Instability (RMI) suppression, a critical challenge in Inertial Confinement Fusion. We evaluate on two complementary settings: running a hydrodynamics simulations on HPC systems, and using a pre-trained machine learning surrogate for rapid design exploration. Our results demonstrate that the MADA system successfully executes iterative design refinement, automatically improving designs toward optimal RMI suppression with minimal manual intervention. Our framework reduces cumbersome manual workflow setup, and enables automated design exploration at scale. More broadly, it demonstrates a reusable pattern for coupling reasoning, simulation, specialized tools, and coordinated workflows to accelerate scientific discovery.

Discovering high-entropy alloy (HEA) compositions that reliably form a target crystal phase is a high-dimensional inverse design problem that conventional trial-and-error experimentation and forward-only machine learning models cannot efficiently solve. Here we present a ReAct (Reasoning + Acting) LLM agent that autonomously proposes, validates, and iteratively refines HEA compositions by querying a calibrated XGBoost surrogate trained on 4,753 experimental records across four phases (FCC, BCC, BCC+FCC, BCC+IM), achieving 94.66% accuracy (F1 macro = 0.896). Against Bayesian optimisation (BO) and random search baselines, the full-prompt agent achieves descriptor-space rediscovery rates of 38%, 18%, and 38% for FCC, BCC, and BCC+FCC (Mann--Whitney $p \leq 0.039$), with proposals lying 2.4--22.8$\times$ closer to the experimental phase manifold than random search. An ablation reveals that domain priors shift the agent from landmark-alloy recall toward compositionally diverse exploration -- an uninformed agent scores higher rediscovery by concentrating on literature-dense families, while the full-prompt agent explores underrepresented space (unique ratio 1.0 vs.\ 0.39 for BCC+FCC). These regimes represent distinct criteria: proximity to known literature versus genuine discovery. Spearman analysis confirms agent reasoning is statistically aligned with empirical phase distributions ($ρ= 0.736$, $p = 0.004$ for BCC). This work establishes LLM-guided agentic reasoning as a principled, transparent, and manifold-aware complement to gradient-free optimisation for inverse alloy design.

Covalent organic frameworks (COFs) are promising photocatalysts for solar hydrogen production, yet the most electronically favorable linkages, imines, hydrolyze rapidly in water, creating a stability--activity trade-off that limits practical deployment. Navigating the combinatorial design space of nodes, linkers, linkages, and functional groups to identify candidates that are simultaneously active and durable remains a formidable challenge. Here we introduce Ara, a large-language-model (LLM) agent that leverages pretrained chemical knowledge, donor--acceptor theory, conjugation effects, and linkage stability hierarchies, to guide the search for photocatalytic COFs satisfying joint band-gap, band-edge, and hydrolytic-stability criteria. Evaluated against random search and Bayesian optimization (BO) over a space consisting of candidates with various nodes, linkers, linkages, and r-groups, screened with a GFN1-xTB fragment pipeline, Ara achieves a 52.7% hit rate (11.5$\times$ random, p = 0.006), finds its first hit at iteration 12 versus 25 for random search, and significantly outperforms BO (p = 0.006). Inspection of the agent's reasoning traces reveals interpretable chemical logic: early convergence on vinylene and beta-ketoenamine linkages for stability, node selection informed by electron-withdrawing character, and systematic R-group optimization to center the band gap at 2.0 eV. Exhaustive evaluation of the full search space uncovers a complementary exploitation--exploration trade-off between the agent and BO, suggesting that hybrid strategies may combine the strengths of both approaches. These results demonstrate that LLM chemical priors can substantially accelerate multi-criteria materials discovery.

Inverse lithography (ILT) is critical for modern semiconductor manufacturing but suffers from highly non-convex objectives that often trap optimization in poor local minima. Generative AI has been explored to warm-start ILT, yet most approaches train deterministic image-to-image translators to mimic sub-optimal datasets, providing limited guidance for escaping non-convex traps during refinement. We reformulate mask synthesis as conditional sampling: a generator learns a distribution over masks conditioned on the design and proposes multiple candidates. The generator is first pretrained with WGAN plus a reconstruction loss, then fine-tuned using Group Relative Policy Optimization (GRPO) with an ILT-guided imitation loss. At inference, we sample a small batch of masks, run fast batched ILT refinement, evaluate lithography metrics (e.g., EPE, process window), and select the best candidate. On LithoBench dataset, the proposed hybrid framework reduces EPE violations under a 3,nm tolerance and roughly doubles throughput versus a strong numerical ILT baseline, while improving final mask quality. We also present over 20% EPE improvement on ICCAD13 contest cases with 3$\times$ speedup over the SOTA numerical ILT solver. By learning to propose ILT-friendly initializations, our approach mitigates non-convexity and advances beyond what traditional solvers or GenAI can achieve.

Inverse design, particularly geometric shape optimization, provides a systematic approach for developing high-performance nanophotonic devices. While numerous optimization algorithms exist, previous global approaches exhibit slow convergence and conversely local search strategies frequently become trapped in local optima. To address the limitations inherent to both local and global approaches, we introduce BONNI: Bayesian optimization through neural network ensemble surrogates with interior point optimization. It augments global optimization with an efficient incorporation of gradient information to determine optimal sampling points. This capability allows BONNI to circumvent the local optima found in many nanophotonic applications, while capitalizing on the efficiency of gradient-based optimization. We demonstrate BONNI's capabilities in the design of a distributed Bragg reflector as well as a dual-layer grating coupler through an exhaustive comparison against other optimization algorithms commonly used in literature. Using BONNI, we were able to design a 10-layer distributed Bragg reflector with only 4.5% mean spectral error, compared to the previously reported results of 7.8% error with 16 layers. Further designs of a broadband waveguide taper and photonic crystal waveguide transition validate the capabilities of BONNI.

The RNA inverse folding problem aims to identify nucleotide sequences that preferentially adopt a given target secondary structure. While various heuristic and machine learning-based approaches have been proposed, many require a large number of sequence evaluations, which limits their applicability when experimental validation is costly. We propose a method to solve the problem using a factorization machine with quadratic-optimization annealing (FMQA). FMQA is a discrete black-box optimization method reported to obtain high-quality solutions with a limited number of evaluations. Applying FMQA to the problem requires converting nucleotides into binary variables. However, the influence of integer-to-nucleotide assignments and binary-integer encoding on the performance of FMQA has not been thoroughly investigated, even though such choices determine the structure of the surrogate model and the search landscape, and thus can directly affect solution quality. Therefore, this study aims both to establish a novel FMQA framework for RNA inverse folding and to analyze the effects of these assignments and encoding methods. We evaluated all 24 possible assignments of the four nucleotides to the ordered integers (0-3), in combination with four binary-integer encoding methods. Our results demonstrated that one-hot and domain-wall encodings outperform binary and unary encodings in terms of the normalized ensemble defect value. In domain-wall encoding, nucleotides assigned to the boundary integers (0 and 3) appeared with higher frequency. In the RNA inverse folding problem, assigning guanine and cytosine to these boundary integers promoted their enrichment in stem regions, which led to more thermodynamically stable secondary structures than those obtained with one-hot encoding.

The inverse design of RNA three-dimensional (3D) structures is crucial for engineering functional RNAs in synthetic biology and therapeutics. While recent deep learning approaches have advanced this field, they are typically optimized and evaluated using native sequence recovery, which is a limited surrogate for structural fidelity, since different sequences can fold into similar 3D structures and high recovery does not necessarily indicate correct folding. To address this limitation, we propose RIDER, an RNA Inverse DEsign framework with Reinforcement learning that directly optimizes for 3D structural similarity. First, we develop and pre-train a GNN-based generative diffusion model conditioned on the target 3D structure, achieving a 9% improvement in native sequence recovery over state-of-the-art methods. Then, we fine-tune the model with an improved policy gradient algorithm using four task-specific reward functions based on 3D self-consistency metrics. Experimental results show that RIDER improves structural similarity by over 100% across all metrics and discovers designs that are distinct from native sequences.

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate step, which is an optimization problem by itself. In many scenarios, several design parameters can lead to the same or similar output values. For such cases, multi-modal probabilistic approaches are advantageous to obtain diverse solutions. A major difficulty in inverse design stems from the structure of the design space, since discrete parameters or further constraints disallow the direct use of gradient-based optimization. To tackle this problem, we propose a novel inverse design method based on diffusion models. Our approach relaxes the original design space into a continuous grid representation, where gradients can be computed by implicit differentiation in the forward simulation. A diffusion model is trained on this relaxed parameter space in order to serve as a prior for plausible relaxed designs. Parameters are sampled by guided diffusion using gradients that are propagated from an objective function specified at inference time through the differentiable simulation. A design sample is obtained by backprojection into the original parameter space. We develop our approach for a composite material design problem where the forward process is modeled as a linear FEM problem. We evaluate the performance of our approach in finding designs that match a specified bulk modulus. We demonstrate that our method can propose multiple diverse designs within 1% relative error margin from medium to high target bulk moduli in 2D and 3D settings. We also demonstrate that the material density of generated samples can be minimized simultaneously by using a multi-objective loss function.

Inverse problems and inverse design in multiphase media, i.e., recovering or engineering microstructures to achieve target macroscopic responses, require operating on discrete-valued material fields, rendering the problem non-differentiable and incompatible with gradient-based methods. Existing approaches either relax to continuous approximations, compromising physical fidelity, or employ separate heavyweight models for forward and inverse tasks. We propose GenPANIS, a unified generative framework that preserves exact discrete microstructures while enabling gradient-based inference through continuous latent embeddings. The model learns a joint distribution over microstructures and PDE solutions, supporting bidirectional inference (forward prediction and inverse recovery) within a single architecture. The generative formulation enables training with unlabeled data, physics residuals, and minimal labeled pairs. A physics-aware decoder incorporating a differentiable coarse-grained PDE solver preserves governing equation structure, enabling extrapolation to varying boundary conditions and microstructural statistics. A learnable normalizing flow prior captures complex posterior structure for inverse problems. Demonstrated on Darcy flow and Helmholtz equations, GenPANIS maintains accuracy on challenging extrapolative scenarios - including unseen boundary conditions, volume fractions, and microstructural morphologies, with sparse, noisy observations. It outperforms state-of-the-art methods while using 10 - 100 times fewer parameters and providing principled uncertainty quantification.

Protein generative models have shown remarkable promise in protein design, yet their success rates remain constrained by reliance on curated sequence-structure datasets and by misalignment between supervised objectives and real design goals. We present ProteinZero, an online reinforcement learning framework for inverse folding models that enables scalable, automated, and continuous self-improvement with computationally efficient feedback. ProteinZero employs a reward pipeline that combines structural guidance from ESMFold with a novel self-derived ddG predictor, providing stable multi-objective signals while avoiding the prohibitive cost of physics-based methods. To ensure robustness in online RL, we further introduce a novel embedding-level diversity regularizer that mitigates mode collapse and promotes sequence-level diversity among generated designs. Within a general RL formulation balancing multi-reward optimization, KL-divergence from a reference model, and diversity regularization, ProteinZero achieves robust improvements across designability, predicted stability, recovery, and diversity. On the CATH-4.3 benchmark, it consistently outperforms state-of-the-art baselines including ProteinMPNN, ESM-IF, and InstructPLM, reducing design failure rates by 36-48% and achieving success rates above 90% across diverse folds. Importantly, a complete RL run can be executed on a single 8xGPU node within three days, including reward computation and data generation. These results indicate that efficient online RL fine-tuning can complement supervised pretraining by allowing protein generative models to evolve continuously from their own outputs and optimize multiple design objectives without labeled data, opening new possibilities for exploring the vast protein design space. Code and model checkpoints are available at https://github.com/ziwenwang28/ProteinZero.