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arXiv2026

M-Tensor Formalism: A Non-iterative High Dimensional Least Squares Regression for Nonlinear Models with Scarce Data

We present a multilinear regression framework based on tensor algebra tailored to high-dimensional contexts where data is scarce. We exploit algebraic properties of a partial tensor product, namely the m-tensor product, to leverage structured equations with separated variables. The proposed method combines kernel properties along with tensor algebra to prevent explicit construction of the exponentially large feature space and tackle approximations up to hundreds of parameters while avoiding the fixed-point strategy. This is achieved by only ever employing the regression operator in a factorized form. We present this formalism along with different regularization techniques suited for low amount of data with a high number of parameters while preserving well-known matrix-based properties. We demonstrate complexity scaling on a general benchmark to show robustness for engineering problems and ease of implementation.

cs.CE↗

arXiv2026

A non-intrusive approach to index-aware learning

We present a non-intrusive version of the index-aware learning framework introduced in arXiv:2309.00958. Index-aware learning itself is an approach for learning the time and parameter dependent solutions of differential-algebraic equations (DAEs), in particular those describing electric circuits. A central feature of the approach is that it ensures the learned solutions to fulfill the inherent constraints of the DAE, such as e.g. Kirchhoff's laws in the case of electric circuits. This is achieved by leveraging a decoupling of the DAE into its differential and algebraic parts, with the non-intrusive version of the approach additionally relying on results from arXiv:2604.20475 and arXiv:2107.07755. We illustrate the approach using a filtered buck converter as an example and compare both the intrusive and non-intrusive versions. The code for the example is openly available.

cs.CE↗

arXiv2026

A Methodology for Integrating Life Cycle Assessment into a Multidisciplinary Design Analysis and Optimization Framework for Sustainable Launcher Development

The increasing number of orbital and sub-orbital launches makes it necessary to investigate the environmental impacts of launch vehicles and incorporate eco-design considerations into their development. In response, the European Space Agency has promoted Life Cycle Assessment (LCA) as a standardization methodology to mitigate environmental impacts of present and future space missions. This need is further amplified in the NewSpace, where numerous configurations and innovative technologies are explored, reinforcing the importance of integrating environmental considerations. At early design stages, launch vehicle architecture can be formalized through a multi-physics optimization problem based on Multidisciplinary Design Analysis and Optimization (MDAO) methods, where disciplines such as propulsion, aerodynamics, structure, and trajectory are coupled to obtain trade-offs among candidate configurations. This paper proposes a methodology to integrate an LCA discipline within an MDAO framework for launch vehicle design. The approach relies on parametric life-cycle inventories depending on design and coupling variables, covering component and propellant production as well as transport to the launch site. Launch emissions are evaluated from optimized trajectory profiles and characterized in terms of climate change impact. The methodology is illustrated on a representative expendable launch vehicle, where multi-objective optimizations assess trade-offs between performance and environmental indicators. Results highlight antagonistic behaviors among environmental impact categories, emphasizing the importance of carefully defining environmental objectives in eco-design studies. The generic nature of the methodology lays the foundation for integrating LCA into early-stage launch vehicle design, enabling exploration of trade-offs between performance, cost, and environmental considerations.

math.OC↗

arXiv2026

FaVOR: LLM-Based Agentic Framework for Factor Mining via Empirical Validation

Traditional finance relies on experts to hand-craft factors through a principled process grounded in economic rationale. Recent LLM-based multi-agent systems have automated this process, scaling factor mining far beyond manual effort. However, these automated approaches optimize directly for returns and rarely check whether a generated factor still expresses the economic hypothesis that motivated it. We identify this inconsistency between mathematical form and economic meaning as a structural failure mode of return-oriented automation. The resulting factors blur the line between real signals and spurious correlations and break down across regime shifts. We propose FaVOR (Factor Validation through Observable Reasoning), an agentic framework that restructures factor mining around hypothesis-level evidence rather than return outcomes. In place of the standard hypothesis-to-formula leap, FaVOR enforces a three-stage consistency loop tying mathematical form to economic rationale throughout. (1) Decomposition splits a broad economic hypothesis into independent observable conditions. (2) Validation checks whether each factor reflects its intended condition. (3) Integration merges them into a composite whose structure remains interpretable. On the CSI 500 and S&P 500 in 2025, FaVOR outperforms existing baselines while remaining effective across regimes. FaVOR shows that hypothesis-grounded factor discovery produces signals that are interpretable by construction, regime-robust, and economically faithful. The code is available at https://github.com/damilab/FaVOR.

cs.AI↗

arXiv2026

Redefining Stablecoins from Nominal to Real Value: A Maximum Likelihood Approach

Stablecoins, typically pegged to fiat currencies, cannot achieve true stability because they inherit fluctuations in the underlying unit of account. To overcome this limitation, we introduce a stablecoin pegged to the Maximum Likelihood Value (MLV), a newly defined unit of account derived as the most probable configuration of latent real-value movements that explains observed nominal-value (price) changes. Grounded in inferential statistics and modern portfolio theory, MLV represents the most stable unit of account, as it enforces a zero real return on the minimum-variance portfolio. Empirical results confirm the operational viability of an MLV-pegged stablecoin: MLV can be computed in real time from 500 asset price series and improves annualized returns and Sharpe ratios while substantially reducing turnover in portfolio optimization.

cs.CE↗

arXiv2026

Sensitivity Hot Spot Penalization: A Robust Topology Optimization Framework against First-Order Worst-Case Perturbations

Deterministic topology optimization can efficiently generate high-performance structural designs, but it does not explicitly control localized fragility induced by manufacturing variations and geometric uncertainties. Such fragility often appears as stress concentrations or hinge-like deformation mechanisms. Conventional robust topology optimization can suppress these features, but typically requires multiple design realizations and substantially increased computational cost. Recent work by Sigmund et al. (2026) introduced sensitivity hot spot penalization (SHoSP), which augments the nominal objective by a smooth maximum of its sensitivities and suppresses localized fragile features at low additional cost while promoting more even stress distributions. This paper establishes a general connection between SHoSP and a first-order worst-case robust approximation under a material-mass perturbation budget using a Taylor expansion and H{"o}lder's duality. The original penalty weight is identified as a dimensionless norm-bounded perturbation budget relative to the area (2D) or volume (3D) of the design domain. This interpretation explains the suppression of sensitivity hot spots, hinge localization, and stress concentrations by limiting the maximum first-order degradation under budgeted perturbations. It is investigated for compliance minimization and compliant mechanism design. Robustness is assessed using a relaxed worst-case density perturbation and by comparing deterministic and SHoSP designs under equivalent perturbation budgets. Stress-related effects observed on structured meshes are cross-validated by stress-oriented topology optimization and body-fitted finite element analyses. Extensions to porous infill optimization, multiple load cases, and large-scale 3D examples further demonstrate the applicability and superior scalability of the SHoSP framework.

cs.CE↗

arXiv2026

Finite Element Model Updating-based Load Rating of Bridges with Incomplete As-Built Information

Load rating is the engineering process of determining the safe load-carrying capacity of an existing bridge structure often through analysis of its load-bearing members and their cross sections. However, when structural drawings and details of the structure are missing or insufficient for such calculations, alternative solutions must be used to infer the capacity. This study proposes a rational and consistent engineering solution for capacity inference based on structural identification (St-Id). The proposed approach uses finite element model updating (FEMU) to estimate the unknown characteristics of structures for use in an analytical load rating, which requires the development of an initial model developed in ABAQUS that can be updated based on experimental test data. ABAQUS allowed for the development of an interface with MATLAB, which facilitated the integration of an automatic iterative parameter optimization algorithm. The optimization algorithm developed in this investigation incorporated the features of a genetic algorithm (GA) and a gradient-based scheme to iterate on the unknown parameters. The proposed approach was evaluated on four in-service highway bridges including two concrete slab and two T-beam structures in varying deterioration condition states, which had sufficient plans available but were treated as having varying degrees of unknown details. The results illustrated that the finite element (FE) model updating approach generated load ratings that were within 0-17% of the target load ratings while alleviating the main challenges of the existing alternatives.

cs.CE↗

arXiv2026

Viable Pool Sizing for On-Chain FX Liquidity: Amplification, Capital, and Resilience

Financial institutions deploying on-chain FX liquidity face a joint design problem: how much capital to commit, and how to configure the pool, to remain both competitive on trading costs and profitable as a liquidity provider? The StableSwap mechanism (Egorov, 2020) interpolates between constant-product (CPMM) and constant-sum (CSMM) market makers (Port and Tiruviluamala, 2022) via an amplification factor A, but neither extreme suits institutional FX: CPMM pools require excessive capital and generate high impermanent loss; CSMM pools are capital-efficient near the peg but drain rapidly under adversarial flow. Using a Merton jump-diffusion price process (Merton, 1976) and the loss-versus-rebalancing (LVR) framework (Milionis et al., 2022), we map the joint (A, TVL) space to identify configurations that satisfy all three institutional requirements: competitive slippage, positive return, and shock resilience. Minimum viable pool size scales approximately as TVL/Q = 1000/A; ROC at that minimum is thin (about 0.054% per horizon) and independent of A; low-A pools (A <= 10) suffer slippage exceeding 200 bps under a 10x shock, while high-A pools (A >= 500) suffer reserve drain up to 60%, establishing both a capital floor and a practical amplification ceiling.

cs.CE↗

arXiv2026

Solving the Incompressible Navier-Stokes Equations on Oriented Curved Surfaces Discretized by Point Clouds

We present a meshfree numerical solver for the incompressible Navier-Stokes equations on oriented curved surfaces that are represented by surface point clouds. On curved surfaces, numerical challenges pertaining to stiffness and pressure-velocity coupling are exacerbated. Moreover, vector calculus on curved surfaces differs from its Euclidean counterpart. The presented method operates on surface point clouds in an Eulerian frame of reference without requiring a computational grid or mesh. It achieves consistent approximation in space and time with high order of accuracy; we demonstrate up to order six. The incompressibility constraint is locally imposed as a weak artificial compressibility approximation, avoiding global matrix inversion. We show that the method provides consistent and convergent approximations of surface vector fields and differential operators. We study the relationship between error, spatial resolution, and artificial Mach number and characterize the frequency spectrum of the artificial oscillations. We provide numerical solutions of the incompressible Navier-Stokes equations on symmetric surfaces, such as the sphere and torus, and on parametric and non-parametric asymmetric surfaces. Since the proposed method works directly on unstructured surface point clouds, it provides a promising approach for simulations on image-derived geometries, such as in biological morphogenesis from microscopy videos.

math.NA↗

arXiv2026

Lightweight Adaptation of EEG Foundation Models for Stroke Motor Imagery Decoding: Domain Shift and Subject-Level Robustness

Motor imagery (MI) electroencephalography (EEG) decoding could support post-stroke rehabilitation, but models developed on healthy cohorts may not transfer reliably to pathological EEG. We evaluated whether Low-Rank Adaptation (LoRA) can efficiently adapt three pretrained EEG foundation models (i.e., LaBraM-base, REVE-base, and REVE-large) for binary left- versus right-hand MI decoding. Frozen-backbone head-only baselines and LoRA adaptation were evaluated using subject-wise five-fold cross-validation on the PhysioNet EEG Motor Movement/Imagery Dataset and a binary subset of the UET175 dataset comprising 30 stroke participants. On EEGMMIDB, LoRA increased accuracy to 0.822 for LaBraM-base and 0.957 for REVE-base. On UET175, all head-only models performed near chance. With LoRA, LaBraM-base remained near chance (0.499$\pm$0.009), whereas REVE-base reached 0.847$\pm$0.194 and outperformed REVE-large (0.806$\pm$0.178), indicating that increased model capacity alone did not improve stroke-domain adaptation. The strongest stroke configuration, REVE-base LoRA, was further evaluated using within-cohort leave-one-subject-out cross-validation (LOOCV), showing 0.952 mean accuracy, but subject-wise accuracy ranged from 0.586 to 1.000, revealing a small low-performing tail. Zero-shot transfer from EEGMMIDB to UET175 remained near chance (0.464$\pm$0.072). These findings show that healthy-benchmark performance does not ensure transfer to stroke EEG. Translation of EEG foundation models to pseudo-online or real-time rehabilitation BCIs should therefore include target-domain adaptation and subject-level assessment of temporal informativeness, spatial sensitivity, and physiological discriminability.

cs.CE↗

arXiv2026

Hidden relationships in a document-derived property graph: top-k chunk embeddings and inverse-distance weighting over a dynamically evolving ontology

Large language models extracting knowledge graphs from text capture only explicitly stated facts, often leaving semantically related entities disconnected across documents. We present an additive, engine-neutral second pass that discovers these latent ties without altering extracted facts. Each document is chunked and embedded once; top-k nearest- neighbor queries across existing chunks yield candidate node pairs via entity membership maps. Candidate pairs are scored using Shepard inverse-distance weighting with a rescaled chord distance metric, avoiding the threshold-collapsing flaw of affine cosine scoring behind a k-NN gate. Un-gated per-pair accumulators form a commutative monoid, ensuring the pipeline is strictly order-independent and scales incrementally without recomputing prior documents. Implemented across FalkorDB, Kinetica, ArangoDB, and Neo4j, our method shows that 768- and 240-dimensional embeddings retain 92% and 72% edge fidelity against a 3072-D baseline while achieving a 25x faster top-k formulation.

cs.CE↗

arXiv2026

MUFASA: An Information Utility-Aware Preprocessing Framework for Reliable Model Reasoning in Computational Pathology

Reliable computational pathology depends on preprocessing methods that identify informative tissue regions while excluding artifacts and low-utility regions from whole-slide images (WSI). However, existing preprocessing pipelines often retain such regions or discard diagnostically relevant tissue, thereby limiting downstream model performance, reliability, and robustness across heterogeneous cohorts. Here, we systematically evaluate how these regions affect downstream AI model performance across multiple clinically relevant applications and introduce MUFASA, a generalizable, information utility-aware preprocessing framework for H&E-stained WSI that excludes artifacts and low-utility regions while preserving biologically meaningful tissue. MUFASA integrates slide-level artifact masking, stain-aware tile filtering, reconstruction-based utility stratification of tiles, and targeted recovery of tissue tiles that are over-filtered by earlier phases. Across tumor diagnosis, tumor subtyping, biomarker status prediction, and survival prognostication tasks in diverse cancer cohorts, MUFASA consistently improves downstream model performance relative to widely used preprocessing baselines. These gains are accompanied by reduced artifact-associated attribution in model heatmaps, indicating improved alignment between retained tissue and model attention. Our findings establish WSI preprocessing as a critical determinant of downstream model performance and validity, revealing that even accurate predictions can conceal important failure modes stemming from anatomically implausible reasoning driven by retained artifact-containing and low information-utility tiles.

cs.CE↗

arXiv2026

Efficient Parameter Calibration of Numerical Weather Prediction Models via Evolutionary Sequential Transfer Optimization

The configuration of physical parameterization schemes in Numerical Weather Prediction (NWP) models plays a critical role in determining the accuracy of the forecast. However, existing parameter calibration methods typically treat each calibration task as an isolated optimization problem. This approach suffers from prohibitive computational costs and necessitates performing iterative searches from scratch for each task, leading to low efficiency in sequential calibration scenarios. To address this issue, we propose the SEquential Evolutionary Transfer Optimization (SEETO) algorithm driven by the representations of the meteorological state. First, to accurately measure the physical similarity between calibration tasks, a meteorological state representation extractor is introduced to map high-dimensional meteorological fields into latent representations. Second, given the similarity in the latent space, a bi-level adaptive knowledge transfer mechanism is designed. At the solution level, superior populations from similar historical tasks are reused to achieve a "warm start" for optimization. At the model level, an ensemble surrogate model based on source task data is constructed to assist the search, employing an adaptive weighting mechanism to dynamically balance the contributions of source domain knowledge and target domain data. Experiments on multiple calibration tasks with varying source--target similarities demonstrate that SEETO consistently improves early-stage calibration efficiency under limited expensive evaluation budgets, while maintaining competitive overall optimization performance. This provides a practical approach for efficient automated calibration of NWP model parameters.

cs.CE↗

arXiv2026

Frontiers in FinTech: Multimodal Foundation Models for Financial Reporting and Decision Science

Financial information no longer arrives in a single format. Research reports come as PDFs, financial statements live in spreadsheets, market trends are captured in images, and policy documents reach analysts as scans, each carrying part of the picture the others cannot supply. Accounting information systems built around single-modality extraction pipelines and rule-based tools therefore struggle to assemble the full picture, slowing financial statement analysis, complicating audit evidence corroboration, and limiting investment decision support. This study presents FinVision, a multimodal large language model that unites vision-language models with domain-specific financial reasoning. Instead of processing documents in isolation, FinVision reads text, tables, and images together, converts them into consistent structured data, and verifies cross-modal agreement, in the same spirit as auditors corroborating evidence from independent sources. The model is trained in two stages, pre-trained on large-scale public financial corpora and fine-tuned on institution-specific investment data, so it can apply established valuation methodologies and audit risk assessment frameworks while outperforming zero-shot and single-stage baselines. A natural-language decision pipeline lets users describe what they need and turns those descriptions into executable workflows, supporting portfolio optimization, real-time risk monitoring, and refinement through multi-turn dialogue. Across 200 listed companies, FinVision reduced valuation error by 19 percent relative to the strongest baseline; a user study with 48 accounting and investment professionals reported a 51 percent reduction in task completion time. These results carry implications for audit automation, financial reporting quality, and more inclusive access to expert-level financial analysis.

cs.CE↗

arXiv2026

QoI-Aware Provisional Rollout and Retrospective Reconciliation for Reduced-State Scientific Twins

Scientific twins may need to continue operating when updates from an authoritative primary system are temporarily unavailable. Once synchronization resumes, the new boundary can also be used to revise the intervening history. We distinguish an immediately available causal provisional trajectory from a delayed, future-conditioned reconciled trajectory. For reduced-state twins, we introduce a deterministic, calibration-based reconciliation method. A smooth temporal bridge carries the residual observed at the next synchronization block backward through the provisional interval. An analytic energy-matching stage then applies smooth regional gains and a global rescaling to match a component-energy trajectory estimated by cubic regression in log-energy space from synchronized frames on both sides of the gap. The method uses no additional correction network and revises decoded history without changing the latent state used for later rollouts. We evaluate 64 spatial patches from 16 JHTDB isotropic-turbulence slices for both velocity components and gaps S in {4, 6, 8}. During the longest gap, field error and gradient-sensitive QoI error degrade at markedly different rates, so field error alone does not characterize provisional fidelity. At S = 8, full reconciliation reduces window-averaged NRMSE by about 60% for both components and global gradient-intensity error from 4.21% to 2.91% for vx, whereas future-aware physical interpolation reaches 20.40% on the same metric. Energy matching additionally makes the reconciled history match its boundary-inferred global energy trajectory exactly. Future boundary information therefore substantially improves scientifically relevant properties within the evaluated regime.

cs.CE↗

arXiv2026

OmniClimate-TC: Physics-Aware Visual Abstractions for Multimedia Reasoning over Tropical Cyclones

Meteorological reanalysis encodes extreme weather through continuous, physically constrained fields, posing a fundamental challenge for vision-language models (VLMs) whose perceptual assumptions are shaped by natural images. Tropical cyclones exemplify this mismatch: critical properties such as intensity extrema, asymmetry, spatial extent, and physical impacts arise from field-level organization rather than object-centric visual cues. Existing approaches address this gap through text alignment or annotation, treating the problem as multimodal supervision rather than representation design. We introduce Physics-Aware Visual Abstraction (PAVA), a plug-and-play physics-aware representation and annotation interface that maps physical reanalysis fields to visually identifiable and semantically grounded perceptual abstractions for supervision and evaluation in vision-language reasoning. Building on PAVA, we construct OmniClimate-TC, a benchmark for tropical cyclone analysis spanning five classes of reasoning and nine tasks, with 243,890 physically grounded instruction-tuning pairs. Using PAVA-aligned supervision, we adapt VLMs and provide evidence that this representation design improves reasoning over tropical cyclone hazard fields. Our results position OmniClimate-TC as a benchmark for multimedia reasoning over structured geophysical fields, and highlight representation design as a key ingredient for physically grounded reasoning in scientific media.

cs.CE↗

arXiv2026

Intrinsic Finite Element Methods for Fluids on Riemannian Manifolds Compared with Surface FEM

We present an intrinsic finite element formulation for the incompressible Navier--Stokes equations on Riemannian manifolds. We derive the corresponding weak formulation and prove that the backward Euler discretisation is energy stable. The proposed framework is validated on several representative manifolds, with particular attention paid to the long-time behaviour of the flow and its convergence to steady-state solutions represented by Killing vector fields. Comprehensive comparisons are performed with the surface finite element method and a corresponding eigenvalue formulation for Killing vector fields. The numerical results demonstrate that the intrinsic formulation provides an accurate, computationally efficient, and geometrically transparent alternative to embedded surface finite element formulations, while naturally extending to higher-dimensional Riemannian manifolds.

cs.CE↗

arXiv2026

Accelerated Patient-Specific Hemodynamic Simulations with Hybrid Physics-Based Neural Surrogates

Physics-based 0D reduced-order models provide computationally lightweight predictions of cardiovascular flows, resolving bulk hemodynamics in fractions of a second that would take days to solve using traditional 3D finite-element techniques. However, the accuracy of 0D models is limited as a result of the dramatic simplifications made in their derivations. In this work, we use 0D parameters learned from high-fidelity 3D data to improve 0D model accuracy without sacrificing its low computational cost or interpretability. We use the resistor-quadratic resistor-inductor (RRI) model to predict pressure drops over 0D vessels and bifurcations, where the resistances and inductance (0D parameters) are predicted from the bifurcation or vessel geometry using neural networks trained on high-fidelity 3D simulations. We validate the hybrid physics-based data-driven framework in three types of patient-specific vasculature - aortic, aortofemoral, and pulmonary anatomies. Use of learned 0D parameters reduces error by at least 50% compared to baseline 0D parameters across all anatomical cohorts. The improvements are especially marked for the more complex pulmonary anatomies, where 0D models with learned parameters reduced error from 30% to 7%. Exclusion of the quadratic resistor in the RRI model improved convergence compared to using the full RRI model. The resulting hybrid model presents a means of real-time (personal laptop runtime of <2 seconds for the most complex pulmonary anatomies), interpretable, and accurate cardiovascular flow modeling, enabling digital twins that support clinical decision-making as well as cardiovascular science and engineering research.

cs.CE↗