Lithography

We propose an all-reflective two-mirror projection system for extreme ultraviolet (EUV) lithography operating at exposure wavelengths of $13.5$~nm (Mo/Si) and $11.2$~nm (Ru/Be), delivering a fourfold ($4\times$) demagnification of the periodic mask pattern at a numerical aperture approaching unity ($\mathrm{NA}_{\max} \approx 0.993$). In contrast to conventional EUV projection objectives that incorporate 6--10 aspheric mirrors with an overall optical throughput of less than $15\%$, the proposed design redirects each accepted discrete spatial diffraction order scattered by the mask onto the wafer via a dedicated pair of planar mirror facets. The number of reflections is strictly fixed at two for all accepted orders, retaining $50$--$60\%$ of the power leaving the mask in each accepted order. We derive a spatial geometry providing rigorous optical path length equalization across all diffraction orders, thereby removing order-dependent propagation phase shifts. Individually optimized 30-bilayer Bragg multilayer coatings are designed for each facet using the transfer matrix method combined with global evolutionary optimization algorithms. The architecture is generalized to a three-dimensional vector formulation with a two-dimensionally periodic mask. Utilizing inverse lithography technology, Fourier parameterization, and a differentiable electromagnetic modal waveguide solver, we solve the synthesis problem for binary absorber masks (La absorber on a Ru/Be/Sr multilayer mirror). We demonstrate simulated aerial images of sub-10-nm features on the wafer (isolated peaks with a full width at half maximum (FWHM) of approximately $5.4$~nm and line pairs with a critical dimension of $6$~nm) and find that the two peaks remain resolved for the tested wafer defocus values from $0$ to $5$~nm along the $z$-axis.

Advances in neural rendering have enabled high-fidelity multi-view reconstruction of 3D scenes. However, free-form non-rigid shape editing remains a significant challenge. Point-based neural representations are highly desirable for multi-view reconstruction because they lack fixed connectivity, which does not constrain the learned surface topology to that of the initialization. Yet this same property causes point-based representations to struggle with holes and surface discontinuities under large deformations. To address this, we propose a novel self-supervised method to enable point-based representations to adapt to large deformations without requiring ground truth multi-view images of deformed geometry. The key idea is to generate random deformations and to ensure consistency in the predicted surface before and after deformation. In particular, the surface prediction from the deformed point cloud should be the same as the deformation applied to the surface prediction from the original point cloud. We incorporate our approach into attention-based point representations, which differ from splatting-based point representations in their use of a learned interpolation kernel between points as opposed to a Gaussian kernel around each point. This learned interpolation kernel can learn to adapt to large deformations, without requiring addition or removal of points. We show that our framework significantly enhances its robustness to large deformations. Experiments on synthetic geometry editing benchmarks (Neural Editor, Objaverse) demonstrate that our approach outperforms existing point-based methods in zero-shot editing and significantly reduces artifacts. Furthermore, qualitative results on the DTU and Mip-NeRF 360 datasets demonstrate our method's effectiveness on real-world scenes.

Automated inspection of small industrial components, including sub-centimetre-scale parts where defects are geometry-driven and poorly resolved by standard optical cameras, calls for sensing modalities that can directly capture fine surface geometry. Vision-based tactile sensors address this need by converting contact imprints into high-resolution image-like data compatible with existing deep-learning pipelines, yet their effective use for industrial anomaly detection (AD) remains largely unexplored. This work systematically evaluates unsupervised AD methods on a real tactile dataset covering five genuine industrial components acquired with a GelSight Mini sensor mounted on a collaborative robot. Four feature-embedding methods, SPADE, PaDiM, FAPM, and InReaCh, are compared under three validations explicitly motivated by the deployment constraints of contact-based sensing: a Good Fraction analysis establishing the minimum number of nominal contacts for stable performance, directly bounded by gel wear since every acquisition degrades the soft interface; a cross-position evaluation assessing generalization across different contact locations observing the same recurring surface pattern; and a low- versus high-resolution comparison evaluating the cost-benefit of higher-resolution tactile acquisition. Overall, this systematic benchmarking study provides practical guidance for researchers and practitioners adopting vision-based tactile sensing for industrial AD and shows how this modality can serve as a viable alternative for industrial quality-control tasks.

We present a theory of textured appearance of optically rough surfaces based on wave optics, emphasizing the role of texture for passive depth from focus. Our theory shows that even surfaces that traditional computer vision would consider textureless can produce textured appearance, due to subjective speckle from surface microgeometry. We analyze the properties of this second-order texture, and show that we can enhance its contrast under natural ambient lighting by simply using a narrowband spectral filter. Doing so results in dramatic improvements in passive depth reconstruction of seemingly textureless scenes, as we demonstrate through extensive theory, simulations, and real-world experiments.

Multimodal large language models have demonstrated strong defect recognition capability in industrial anomaly detection. However, in lithography review, merely determining whether an image contains a defect is insufficient for engineering inspection; models must also understand defect morphology, spatial location, and the potential causes supported by visible evidence. To this end, this paper proposes LDU-Bench, a multi-task multimodal benchmark for lithography defect understanding. Constructed from real lithography and integrated-circuit review images, LDU-Bench decomposes the review workflow into four independent tasks: defect triage, morphology recognition, coarse localization, and image-conditioned cause analysis. It systematically evaluates models using task-level metrics, diagnostic readouts, and the Lithography Closure Score (LCS). Experimental results show that although existing MLLMs can perform defect triage relatively reliably, this ability does not stably transfer to downstream review stages. Morphology alignment, effective localization, and evidence-to-cause mapping remain the major bottlenecks. Further diagnostics indicate that this capability break is not a fluctuation of a single metric, but reflects insufficient structured understanding across semantic levels. Overall, LDU-Bench provides a quantifiable and diagnostic unified platform for evaluating the usability, failure points, and capability boundaries of industrial MLLMs in lithography review chains.

Spatial atomic layer deposition (SALD) is a leading atmospheric-pressure, high-throughput route to industrial ALD, but design and control are limited by the cost of predicting surface coverage: high-fidelity CFD is far too slow for operating-window scans, while analytic models miss transport modulation such as the gas curtain. We present a physics-chemistry-informed neural network (PCINN), a hybrid surrogate with CFD-level accuracy at real-time speed: a query returns coverage in about 7 ms, roughly 5x10^4 times faster than a CFD solve, reaching a test R^2_log = 0.998 (leave-one-out R^2_raw = 0.974) from only 30 training cases spanning four orders of magnitude in coverage. The architecture is not a black box: a small network learns only the operating-condition to near-wall concentration closure, while the known surface kinetics is a hard-coded, trainable chemistry layer integrated along the substrate trajectory. This single-scalar bottleneck keeps it accurate under sparse data, interpretable and invertible. We add a full identifiability analysis (Fisher information, profile likelihood). The adsorption energy E_ads and desorption rate k_des are robustly identifiable; k_ads is not separately identifiable at a single temperature (only k_ads*c_wall is). Across four temperatures the prefactor nu and E_ads bind along a weakly identifiable degeneracy valley of slope 0.065 eV/decade, derived analytically as k_B T_eff ln(10) and turned into a reliability diagnostic: a seven-chemistry mismatch matrix shows it is invariant under any single-Arrhenius mismatch and shifts only when a second thermally activated process appears, so a slope departure flags unmodelled site heterogeneity. Data come from simulation with known ground truth inverted by the same kinetic form, so the study verifies pipeline self-consistency and the identifiability boundary, not real parameters.

Scientific figure comprehension and reasoning using multimodal AI requires integrating visual perception with domain-specific reasoning to extract meaningful knowledge, often not presented in the text of a research publication. The Sci-ImageMiner benchmark dataset, accompanied by a community-driven competition, raises the bar over prior scientific competitions by curating a comprehensive, expert-annotated dataset across four end-to-end complementary tasks. The competition attracted 68 active participants and 1,263 public/private submissions from 9th January 2026 to 8th April 2026. Our results show that state-of-the-art multimodal models perform well on classification and summarization tasks but struggle with data extraction and scientific reasoning, particularly in visual question-answering. These findings reveal key limitations and highlight challenges and opportunities for improving domain-aware multimodal AI systems. Overall, the Sci-ImageMiner benchmark and competition establish a rigorous platform for advancing research in scientific figure comprehension and reasoning and demonstrate the potential of state-of-the-art approaches for a challenging and complex research area.

We present a physics-informed neural operator (PINO) trained with pseudo-spectral frequency-domain (PSFD) equations for electromagnetic (EM) scattering problems in EUV lithography. The Fourier neural operator is factorized into a two-dimensional lateral ($xy$) branch and a one-dimensional axial ($z$) branch and is trained self-consistently with background decomposition.Thus, the full-vector coupling between the mask and the multilayer response is retained without invoking a finite-order Born approximation. In this way, the computational domain size is significantly reduced, thereby lowering the computational cost. The PINO is trained on approximately 16,000 mask designs from the LithoBench library sampled randomly at each training iteration without using precomputed EM field solutions. The PINO surrogate model yields predictions with a mean absolute error of about $7 \times 10^{-3}$ for the scattered intensity of held-out mask patterns relative to the reference PSFD solution. Combined with spectral damping, the PINO warm-start initialization accelerates the background-decomposed PSFD solver on finer discretizations.

Both Remotely Operated underwater Vehicles (ROVs) and Autonomous Underwater Vehicles (AUVs) are frequently deployed to acquire geometric bathymetric data. However, it is often discovered post-survey that the acquired data coverage is incomplete. Given the high operational cost associated with underwater deployments, it is essential to incrementally visualize surface coverage in real-time to support informed decision-making by both the operators of ROVs and the AUVs during data collection. In addition, traditional incremental surface reconstruction methods, such as Digital Terrain Models (DTMs), are inherently limited in expressiveness: they represent surfaces as height fields, allows only one elevation value per $(x, y)$ coordinate and thus cannot capture overhangs or vertical structures. To overcome these limitations, we adapt the original Ball Pivoting Algorithm (BPA) into an incremental, real-time, and free-form surface reconstruction method, referred to as Incremental BPA (IBPA). Our method incrementally constructs an orientable, manifold mesh from streaming point cloud data without imposing assumptions regarding point cloud overlap or spatial distribution. Furthermore, we introduce a hole detection mechanism that identifies and highlights incomplete mesh regions. Compared to existing approaches, our method supports more complex surface topologies without prior structural assumptions. The source code of our reference implementation is available: https://github.com/Mauhing/Incremental-BPA

Recent advances in 3D mesh generation have enabled the creation of visually realistic assets. However, much of their visual fidelity is encoded in textures rather than geometry. When such assets are fabricated using monochromatic materials, texture information is largely lost, causing visually important details to disappear even when the original geometry is faithfully preserved. A key challenge is that the geometric perturbations required to recover texture-dependent appearance cues often introduce sharp local features and high-frequency surface structures, which may increase stress concentration and fabrication risk. In this paper, we present GenMF, an appearance-oriented geometry refinement framework for monochromatic fabrication. GenMF transforms texture-dependent visual cues into geometry-induced shading effects and formulates geometry refinement as a balance between appearance preservation and fabrication-oriented robustness. To discourage structurally and narrow the gap between simulation and physical manufacturing, we further introduce a differentiable stress-aware regularization based on a learned thermal-stress predictor. Experimental results demonstrate that GenMF significantly improves appearance preservation under monochromatic rendering while reducing stress concentration under a consistent thermo-mechanical simulation setting. Physical 3D printing examples further show that the refined geometries preserve more recognizable visual details while remaining suitable for fabrication. These results suggest that appearance-aware geometry refinement provides an effective bridge between generated 3D assets and fabrication-ready monochromatic objects.

As semiconductor technology nodes scale, computational lithography is essential for ensuring yield and performance. However, lithography is a continuous physical process involving mask optimization, optical imaging, resist exposure, and development, which existing models fail to capture. To overcome this limitation, we present LithoDreamer, the first physics-informed World Model (WM) framework for computational lithography, which formulates the ``Layout-Mask-Resist Image-After Development Image (ADI)'' pipeline as a decision-driven multi-step evolution system. LithoDreamer captures feature changes between adjacent states to model stage-specific physics-informed latent spaces, in which it controls process intervention exploration and drives subsequent state transitions. To achieve interpretable intervention optimization without continuous supervision, we propose a contrastive variational optimization paradigm that contrasts the latent differences between intervention paths with variational evolution constraints, guiding the model to generate evolutions consistent with real lithography physics. Experiments show LithoDreamer achieves state-of-the-art performance in forward evolution and inverse planning. Our lithography dataset is publicly available at GitHub (https://github.com/7jiangyq/lithodreamer.git).

Existing texture datasets for tactile sensing primarily consist of sensor readings from a specific sensor interacting with available surfaces/objects rather than describing the textures themselves, limiting fair comparison between tactile sensors and hindering reproducible research. In this work, we introduce a 3D-printable dataset of mathematically defined textures designed to be fabricated reliably across different printers and filament types. The dataset consists of six parametrically generated surface patterns derived from combinations of sine-wave and Fourier-based functions, giving controlled variation in spatial frequency, amplitude, and directional structure. We evaluate the reproducibility of these textures across three popular 3D printers and multiple filament types by measuring variance in images captured using an optical TacTip sensor under controlled contact conditions. Our results show that print quality, particularly peak sharpness and stringing, affects tactile variance, with higher-end printers producing significantly more consistent signatures. Classification experiments using neural networks and PCA-based models further demonstrate that high-quality prints support strong within-printer generalisation, while cross-printer generalisation remains challenging due to geometric inconsistencies. This work establishes the first openly available, physically reproducible 3D-printed texture benchmark, providing a foundation for fair comparison of tactile sensors.

Gradient-based inverse lithography technology~(ILT) for extreme ultraviolet~(EUV) masks is presented. A novel framework treats the differentiable waveguide method and the recently proposed waveguide neural operator~(WGNO) as end-to-end physics engines, recovering the permittivity of the absorber of the mask through automatic differentiation of the full forward diffraction model. Numerical experiments on realistic 2D and 3D absorbers of the mask (TaBN, La, U) at $λ{=}11.2$~nm show that the considered ILT methods make it possible to obtain a mask structure that achieves the desired field on the wafer.

Interest in applying data-driven approaches in manufacturing has grown significantly, particularly for mapping complex, high-dimensional relationships. The milling process is one area where predictive models can link influential parameters to surface roughness metrics prior to in situ operations. While this approach offers clear advantages, it faces challenges due to limited datasets and robustness issues in inverse design paradigms. To address these challenges, this paper proposes a machine learning (ML)-based framework for the inverse design of the surface milling process, with a focus on surface roughness as the design objective. The framework employs forward training of two ML models, a deep neural network (DNN) and a random forest (RF) ensemble, both developed using a high-fidelity synthetic dataset generated from a computational simulation framework. These trained models are integrated into a Bayesian optimization (BO) procedure to overcome the multiplicity problem arising from the many-to-one mapping inherent in the dataset. The approach identifies top-performing milling process configurations, considering both process and tool parameters, and presents them from the full solution space. The models achieve average relative errors below 5% when compared to reference results, thereby demonstrating the robustness and reliability of the proposed methodology.

Spin coating is widely used for fabrication of thin polymer and elastomer films, yet reliable thickness verification of highly compliant materials remains challenging due to deformation from contact-based measurements and the cost and complexity of conventional optical metrology. Accurate thickness control is especially critical in soft elastomer applications such as dielectric elastomer actuators (DEAs), where mechanical and functional performance scales strongly with film thickness. This work presents a low-cost, primarily 3D-printed benchtop spin coater with an integrated, minimally deforming optical thickness measurement system for soft-film fabrication workflows. The system is designed to manufacture films between 50 and 300 microns thick with repeatability within 10 microns. Thickness is measured in-situ by tracking displacement of a reflected laser beam via quadrant photodetector, avoiding significant deformation. Optical geometry, sensor linearity constraints, and structural validation via finite element analysis are discussed. Experimental validation using calibrated metal shims demonstrated a thickness resolution of 3.6-3.7 microns and best-case measurement repeatability of 13 microns (95 percent confidence interval). The platform repeatably produced silicone films within 9 microns of target thickness, demonstrating that accessible optical metrology can be integrated into a low-cost spin coating system for practical, thickness-controlled fabrication of compliant thin films without specialized industrial instrumentation.

Generative models are increasingly used to propose designs, data, and control actions for physical systems, yet many such systems are governed by hard physical constraints rather than by perceptual plausibility. Semiconductor manufacturing provides a demanding test case: generated masks, layouts, synthetic defect data, and process recipes must obey lithography, transport, reaction, and device-physics constraints, because physically invalid samples are not merely low quality but unusable. This Perspective argues that semiconductor manufacturing exposes a broader computational-science challenge, namely that generative AI for constrained physical domains must be physics-informed by construction, not corrected only through post-hoc filtering. We survey the emerging architectural toolkit, including physics-informed diffusion, PDE-constrained variational models, neural-operator priors, and conservation-law-respecting generative networks, and show how it connects to differentiable lithography, TCAD, process simulation, and autonomous experimentation. We identify four integration patterns between generative models and physics-based simulators, and we propose a research agenda centered on physics-fidelity benchmarks, differentiable simulator infrastructure, and multimodal foundation models for physical design and manufacturing. The central claim is analytical rather than rhetorical: where physical validity is the binding criterion of success, architectures that enforce it by construction should be expected to outperform those that filter for it after the fact, and the fab is the setting where this distinction is sharpest.

Semiconductor lithography inspection requires reliable detection of small pattern defects such as bridge, burr, pinch, and contamination. In this study, we propose a two-stage vision-language framework that combines initial defect detection with prediction refinement. In the first stage, Qwen3-VL is fine-tuned with LoRA as a vision-language adapter to predict defect counts, defect categories, and normalized bounding boxes from lithography images. However, direct fine-tuning may still produce common test-time errors, including false positives, missed defects, and incorrect defect types. To address this limitation, the second stage trains a refinement module using first-stage prediction failures and their corrected labels, allowing the model to review and revise initial outputs. By learning from cases where the initial adapter fails, the refinement process improves defect inference beyond single-stage fine-tuning.

Reliable polymer identification is essential for ensuring the quality and safety of recycled plastics, yet conventional sorting and spectroscopic techniques often struggle to deliver robust discrimination. Terahertz (THz) spectroscopy offers a promising alternative, providing high-resolution and non-destructive measurements. In this work, we leverage THz signals to classify 12 types of polymers, including pure polymers, multilayer films, commercial blends, and biopolymers. To handle the complexity of these spectral signals, we propose the Multi-Scale Feature Attention Network (MSFAN), a novel deep learning architecture tailored for THz data. The framework integrates feature gating for signal recalibration and multi-scale parallel convolutions to capture diverse frequency patterns. These features are further refined through cross-feature attention and attention pooling, enabling the model to intrinsically highlight the most informative THz regions. MSFAN consistently outperforms state-of-the-art models, reaching a classification accuracy of 85.2%. This study demonstrates the potential of combining THz spectroscopy with deep learning techniques for effective, scalable, and interpretable polymer classification.

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.

Recent feedforward 3D reconstruction methods predict point maps and estimate global 3D geometry remarkably well. However, their predictions still exhibit inaccurate local surface geometry, which is clearly visible qualitatively but only weakly reflected in common metrics. To make these errors more explicit in evaluation, we introduce a point map normal metric that evaluates the local surface orientation induced by neighboring 3D predictions. To reduce these errors, we propose two complementary components: a point gradient matching loss that supervises depth-normalized 3D finite differences, and a Neighborhood Attention Decoder (NAD) that progressively upsamples features and uses Neighborhood Attention for local feature mixing. Across eight zero-shot monocular geometry benchmarks, our model, SurGe, achieves the best average rank for global point map AbsRel and consistently improves local point map and point map normal evaluations.

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.

Open surface components prevail in real industrial 3D content and support rendering, physical simulation and geometric editing. Garments serve as a typical open surface type, with numerous existing generation methods leveraging sewing patterns to generate 2D panels and stitch them into 3D shapes. Such domain-specific designs lack scalability and cannot generalize to shoes and accessories. Common field-based 3D generators prioritize watertight meshes and tend to create flawed double-layer structures on open surfaces. Though Trellis2 adopts field-free representation, its open surface results still contain normal and topology errors. We present AnySurf, a unified framework generating open, closed and hybrid 3D surfaces with accurate face orientation. Built on directed-edge enhanced Flexible Dual Grid (FDG-D), our representation retains normal direction information via oriented grid edges. We also propose ROS-FT post-training and a lightweight DE-Adapter with merely 1% extra parameters, facilitating directed edge learning while preserving original generation performance. We further construct Outfit3D dataset containing industrial garments and closed accessories. Our work transforms garment modeling into a universal 3D generation task. Experimental results demonstrate superior mesh quality and better practicality for downstream applications.

The growing adoption of lattice-based structures in soft robotics creates a need for advanced sensing solutions capable of monitoring their global deformation, particularly compression and extension. In this work, we address this challenge by introducing a novel optical sensor based on two patterned waveguides arranged in an ellipsoidal geometry. This Bidirectional Optical sensor for Actuation Tracking (BOAT) is seamlessly co-printed with a lattice structure actuated by an embedded pneumatic artificial muscle (PAM), and its performance is assessed. During PAM elongation or contraction, the bending of the embedded BOAT waveguides induces output signal variations that enable a clear discrimination between compression and extension states. The designs of both each specific waveguide structure (by surface patterning) and of the sensorized lattice-based unit embedding two BOATs are supported by numerical simulations. Experimental calibration over 100 consecutive pressure cycles ranging from +50 kPa to $-$40 kPa demonstrates a highly repeatable response, allowing a reliable distinction between extension and compression. Finally, sensor feedback is used to implement a digital shadow, enabling continuous synchronization between the whole sensorized unit and its virtual counterpart. These results establish BOAT as a powerful and reliable approach for deformation monitoring in soft lattice-based robotic systems.

As time-to-market is crucial in the Integrated Circuit (IC) industry, speeding up layout manufacturability verifi-cation is essential. Chemical-Mechanical Polishing (CMP) plays a vital role in IC fabrication but is significantly influenced by Layout-Dependent Effects (LDE). An accurate and efficient CMP model enables design teams to correct surface unevenness before fabrication, reducing costs and accelerating the design phase. However, existing models often rely on Density Step Height (DSH) modeling, which is time-consuming for calibration and requires substantial hardware resources for fine-grained predictions. In this paper, we propose combining the advantages of two surface analysis techniques, White Light Interfer-ometry (WLI) and Atomic Force Microscopy (AFM), to train a deep learning model. This model aims to predict full-chip post-CMP nanotopography with nanometer-scale accuracy. Our deep learning model is based on a Convolutional Neural Network (CNN) and follows a two-step pipeline. The model is trained on each technique separately, resulting in a detailed full-chip CMP model.

Calibrating the urban underlying surface parameters is crucial for urban flood simulation. We formulate the parameter calibration problem into an optimization problem within the Bayesian framework using the maximum likelihood principle. We adopt the urban flood dynamical system model as the surrogate model and innovatively introduce latent variables inspired by machine learning to represent more uncertainties, which can also be compatible with common physical parameter calibration. For more efficient optimization, we construct the adjoint equation of the surrogate model to obtain gradient information and propose the parameter sharing technique and the localization technique to reduce the computation complexity of the adjoint equation. A simple case verifies the proposed method can converge quickly and is insensitive to the observation time interval. In the case derived from Test 8A, we calibrate Manning's coefficient of urban roads, with a maximum relative error of 13.88% and a minimum of 1.16%.

Large language models are increasingly deployed in settings where reliability matters, yet output-level uncertainty signals such as token probabilities, entropy, and self-consistency can become brittle under calibration--deployment mismatch. Conformal prediction provides finite-sample validity under exchangeability, but its practical usefulness depends on the quality of the nonconformity score. We propose a conformal framework for LLM question answering that uses internal representations rather than output-facing statistics: specifically, we introduce Layer-Wise Information (LI) scores, which measure how conditioning on the input reshapes predictive entropy across model depth, and use them as nonconformity scores within a standard split conformal pipeline. Across closed-ended and open-domain QA benchmarks, with the clearest gains under cross-domain shift, our method achieves a better validity--efficiency trade-off than strong text-level baselines while maintaining competitive in-domain reliability at the same nominal risk level. These results suggest that internal representations can provide more informative conformal scores when surface-level uncertainty is unstable under distribution shift.