The multiphase-field method is widely used to simulate the evolution of complex microstructures in computational materials science and is commonly derived via a variational approach. When coupled with heat conduction, it is desirable to derive both the multiphase-field method and the heat conduction equation from a unified, consistent framework. In the present work, this is accomplished by introducing order parameters as internal state variables and exploiting the entropy production inequality of the diffuse interface region for multiple intersecting phases. The approach represents a generalization of the method of Prahs et al. (Prahs et al. Continuum Mech. Thermodyn. 37, 55 (2025). https://doi.org/10.1007/s00161-025-01383-y ) via a dual-interaction ansatz and its Lagrange multiplier simplification, while maintaining thermodynamical consistency. This requirement, in turn, restricts the choice of the interpolation functions. Moreover, the coupling effects in the heat conduction equation as well as connections to established evolution equations from the literature are demonstrated through an illustrative derivation.
We present HI-SLAM2, a geometry-aware Gaussian SLAM system that achieves fast and accurate monocular scene reconstruction using only RGB input. Existing Neural SLAM or 3DGS-based SLAM methods often trade off between rendering quality and geometry accuracy, our research demonstrates that both can be achieved simultaneously with RGB input alone. The key idea of our approach is to enhance the ability for geometry estimation by combining easy-to-obtain monocular priors with learning-based dense SLAM, and then using 3D Gaussian splatting as our core map representation to efficiently model the scene. Upon loop closure, our method ensures on-the-fly global consistency through efficient pose graph bundle adjustment and instant map updates by explicitly deforming the 3D Gaussian units based on anchored keyframe updates. Furthermore, we introduce a grid-based scale alignment strategy to maintain improved scale consistency in prior depths for finer depth details. Through extensive experiments on Replica, ScanNet, Waymo Open, ETH3D SLAM and ScanNet++ datasets, we demonstrate significant improvements over existing Neural SLAM methods and even surpass RGB-D-based methods in both reconstruction and rendering quality.
Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to local non-stationarity. We show that this adaptation induces a critical trade-off between the minimum attainable p-value and its stability. As importance weights localize to relevant calibration instances, the effective sample size decreases. This can render standard conformal p-values overly conservative for effective error control, while the smoothing technique used to mitigate this issue introduces conditional variance, potentially masking anomalies. We propose a continuous inference relaxation that resolves this dilemma by decoupling local adaptation from tail resolution via continuous weighted kernel density estimation. While relaxing finite-sample exactness to asymptotic validity, our method eliminates Monte Carlo variability and recovers the statistical power lost to discretization. Empirical evaluations confirm that our approach not only restores detection capabilities where discrete baselines yield zero discoveries, but outperforms standard methods in statistical power while maintaining valid marginal error control in practice.
Recent advances in generative modeling have substantially enhanced novel view synthesis, yet maintaining consistency across viewpoints remains challenging. Diffusion-based models rely on stochastic noise-to-data transitions, which obscure deterministic structures and yield inconsistent view predictions. We propose a Data-to-Data Flow Matching framework that learns deterministic transformations directly between paired views, enhancing view-consistent synthesis through explicit data coupling. To further enhance geometric coherence, we introduce Probability Density Geodesic Flow Matching (PDG-FM), which constrains flow trajectories using geodesic interpolants derived from probability density metrics of pretrained diffusion models. Such alignment with high-density regions of the data manifold promotes more realistic interpolants between samples. Empirically, our method surpasses diffusion-based NVS baselines, demonstrating improved structural coherence and smoother transitions across views. These results highlight the advantages of incorporating data-dependent geometric regularization into deterministic flow matching for consistent novel view generation.
Photosynthetically active radiation (PAR) sensors are widely used in plant stress monitoring, ecophysiology, and forest growth modeling. Recently, multi-spectral PAR sensors have emerged as practical alternatives to established single-channel systems. These sensors offer significant potential, given their competitive accuracy to commercial systems and additional capability to obtain spectral information. This work introduces a new calibration framework specifically tailored for multi-spectral sensors. Previous approaches were only accurate and reliable under identical light conditions. Our calibration setup within a controlled environment ensures consistency and reproducibility of the sensor calibration in every ambient light condition. A dedicated data acquisition and preprocessing framework accounts for spectral characteristics of each component, forming the basis for the Partial Least Squares (PLS) calibration model. This fits the multi-spectral data to the ideal quantum response and enables robust modeling even in case of high collinearity among input variables. With only one calibration coefficient for each channel, a highly efficient implementation of the PAR calculation is possible. Moreover, the method compensates for the spectral leakage of the NIR in the visual range channels. The spectral accuracy of the calibration model is demonstrated by presenting, for the first time, the quantum response curve of a calibrated multi-spectral PAR sensor. In addition, a field validation experiment is conducted under variable weather conditions to assess the absolute performance. With an error of 2.43% relative to a commercial sensor, this work highlights the accuracy achieved with the proposed calibration method. For further investigation, this work provides a repository with data from our calibration setup.
