arXiv subjects

Henrik Christiansen

Publications and source records attributed to Henrik Christiansen.

At least 19 recordsLinked to original sources

arXiv2026

BU-MBAR: A hybrid solution strategy for the MBAR equations

The multi-state Bennett acceptance ratio (MBAR) equations combine the data collected under different thermodynamic conditions in a statistically optimal way. Due to their practical importance, several solution strategies have been devised to optimize the convergence of the resulting set of coupled equations. However, even with graphics processing unit (GPU) acceleration, the convergence of these methods can still be either unstable or slow. We propose a new approach where the equations are interpreted as the limit of infinitesimal bin width of the respective weighted histogram analysis method (WHAM). In the proposed binned-to-unbinned MBAR (BU-MBAR) method, the bin width is adapted dynamically to ensure a stable and efficient convergence to the asymptotic solution.

physics.comp-ph↗

arXiv2026

Hyperspatial Sampling: Circumventing Free-Energy Barriers via Replica Exchange with Extra Dimensions

Simulating systems with rugged free-energy landscapes remains a central challenge in computational physics and chemistry. We introduce hyperspatial replica exchange (HS-REX), an enhanced sampling method in which the physical system is artificially extended by additional spatial dimensions. In higher dimensions, free-energy barriers can be circumvented through paths that are geometrically inaccessible in the original space. Restricting the penalty to only solute atoms dramatically reduces the number of replicas required for solvated systems compared to standard temperature replica exchange, a feature especially relevant for biological applications. As proof of concept, we demonstrate the method on a double-well model system and on alanine dipeptide in explicit water as benchmark system. In the latter case, HS-REX achieves enhanced conformational sampling of not only the slow backbone dihedral angles, but also both chiral configurations of the molecule, which are sterically inaccessible to standard sampling in three dimensions. This demonstrates enhanced ergodic sampling over conventional temperature replica exchange.

physics.comp-ph↗

arXiv2026

On the limits and opportunities of AI reviewers: Reviewing the reviews of Nature-family papers with 45 expert scientists

With the advancement of AI capabilities, AI reviewers are beginning to be deployed in scientific peer review, yet their capability and credibility remain in question: many scientists simply view them as probabilistic systems without the expertise to evaluate research, while other researchers are more optimistic about their readiness without concrete evidence. Understanding what AI reviewers do well, where they fall short, and what challenges remain is essential. However, existing evaluations of AI reviewers have focused on whether their verdicts match human verdicts (e.g., score alignment, acceptance prediction), which is insufficient to characterize their capabilities and limits. In this paper, we close this gap through a large-scale expert annotation study, in which 45 domain scientists in Physical, Biological, and Health Sciences spent 469 hours rating 2,960 individual criticisms (each targeting one specific aspect of a paper) from human-written and AI-generated reviews of 82 Nature-family papers on correctness, significance, and sufficiency of evidence. On a composite of all three dimensions, a reviewing agent powered by GPT-5.2 scores above each paper's top-rated human reviewer (60.0% vs. 48.2%, p = 0.009), while all three AI reviewers (including Gemini 3.0 Pro and Claude Opus 4.5) exceed the lowest-rated human across every dimension. AI reviewers' accurate criticisms are also more often rated significant and well-evidenced, and surface a distinct 26% of issues no human raises. However, AI reviewers overlap far more than humans do (21% vs. 3% for cross-reviewer pairs), and exhibit 16 recurring weaknesses humans do not share, such as limited subfield knowledge, lack of long context management over multiple files, and overly critical stance on minor issues. Overall, our results position current AI reviewers as complements to, not substitutes for, human reviewers.

cs.CL↗

arXiv2026

Variational Kolmogorov-Arnold Network

Kolmogorov-Arnold Networks (KANs) offer a theoretically grounded alternative to multi-layer perceptrons by representing multivariate functions as compositions of univariate basis functions. However, a critical limitation of KANs is the need to manually specify the number of basis functions per layer -- a hyperparameter that directly controls model capacity and substantially impacts performance, yet whose optimal value varies unpredictably across tasks. We present InfinityKAN, a variational inference framework that eliminates this design choice by learning the number of basis functions during training. Our approach models the basis count as a latent variable with a truncated exponential prior, introducing a differentiable weighting function that enables gradient-based optimization. We establish the Lipschitz continuity of the variational objective, ensuring stable training dynamics. Experiments across 18 datasets spanning synthetic, image, tabular, and graph domains demonstrate that InfinityKAN matches or exceeds the performance of KANs while requiring no manual selection of the number of bases for each layer.

cs.LG↗

arXiv2026

Logical Guidance for the Exact Composition of Diffusion Models

We propose LOGDIFF (Logical Guidance for the Exact Composition of Diffusion Models), a guidance framework for diffusion models that enables principled constrained generation with complex logical expressions at inference time. We study when exact score-based guidance for complex logical formulas can be obtained from guidance signals associated with atomic properties. First, we derive an exact Boolean calculus that provides a sufficient condition for exact logical guidance. Specifically, if a formula admits a circuit representation in which conjunctions combine conditionally independent subformulas and disjunctions combine subformulas that are either conditionally independent or mutually exclusive, exact logical guidance is achievable. In this case, the guidance signal can be computed exactly from atomic scores and posterior probabilities using an efficient recursive algorithm. Moreover, we show that, for commonly encountered classes of distributions, any desired Boolean formula is compilable into such a circuit representation. Second, by combining atomic guidance scores with posterior probability estimates, we introduce a hybrid guidance approach that bridges classifier guidance and classifier-free guidance, applicable to both compositional logical guidance and standard conditional generation. We demonstrate the effectiveness of our framework on multiple image and protein structure generation tasks.

cs.LG↗

arXiv2026

A Leibniz rule of distributional pairing and hyperforce sum rule

We reformulate and generalize the equilibrium hyperforce sum rule, a generalization of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy, by employing the Schwartz space and its dual. We show that the hyperforce sum rule for the Euclidean space and the equilibrium BBGKY hierarchy at arbitrary level are derived through the Leibniz rule of the derivative for the pairing of tempered distributions and Schwartz functions. We also apply the Leibniz rule to obtain the hyperforce sum rule for systems with periodic boundary conditions.

math-ph↗

arXiv2026

Adaptive Width Neural Networks

For almost 70 years, researchers have typically selected the width of neural networks' layers either manually or through automated hyperparameter tuning methods such as grid search and, more recently, neural architecture search. This paper challenges the status quo by introducing an easy-to-use technique to learn an unbounded width of a neural network's layer during training. The method jointly optimizes the width and the parameters of each layer via standard backpropagation. We apply the technique to a broad range of data domains such as tables, images, text, sequences, and graphs, showing how the width adapts to the task's difficulty. A by product of our width learning approach is the easy truncation of the trained network at virtually zero cost, achieving a smooth trade-off between performance and compute resources. Alternatively, one can dynamically compress the network until performances do not degrade. In light of recent foundation models trained on large datasets, requiring billions of parameters and where hyper-parameter tuning is unfeasible due to huge training costs, our approach introduces a viable alternative for width learning.

cs.LG↗

arXiv2025

Fast, Modular, and Differentiable Framework for Machine Learning-Enhanced Molecular Simulations

We present an end-to-end differentiable molecular simulation framework (DIMOS) for molecular dynamics and Monte Carlo simulations. DIMOS easily integrates machine-learning-based interatomic potentials and implements classical force fields including an efficient implementation of particle-mesh Ewald. Thanks to its modularity, both classical and machine-learning-based approaches can be easily combined into a hybrid description of the system (ML/MM). By supporting key molecular dynamics features such as efficient neighborlists and constraint algorithms for larger time steps, the framework makes steps in bridging the gap between hand-optimized simulation engines and the flexibility of a \verb|PyTorch| implementation. We show that due to improved linear instead of quadratic scaling as function of system size DIMOS is able to obtain speed-up factors of up to $170\times$ for classical force field simulations against another fully differentiable simulation framework. The advantage of differentiability is demonstrated by an end-to-end optimization of the proposal distribution in a Markov Chain Monte Carlo simulation based on Hamiltonian Monte Carlo (HMC). Using these optimized simulation parameters a $3\times$ acceleration is observed in comparison to ad-hoc chosen simulation parameters. The code is available at https://github.com/nec-research/DIMOS.

physics.comp-ph↗

arXiv2025

Influence of Thermostats on the Dynamics of the Helix-Coil Transition

We present results from all-atom molecular dynamics simulations for the nonequilibrium dynamics of the collapse and helix-coil transition in polyalanine. In particular, we compare the influence of three different thermostats, viz., the Langevin, Andersen, and Nosé-Hoover thermostats. For that purpose, we investigate the nonequilibrium pathways of the transition from the high-temperature random-coil state to the low-temperature helical state. Additionally, we analyze the time evolution of the potential energy and temperature. Our results show only small differences in the observed phenomenology, albeit quantitatively the dynamics appear to be different for the three thermostats.

cond-mat.soft↗

arXiv2025

Nonequilibrium Dynamics of the Helix-Coil Transition in Polyalanine

In this work, the nonequilibrium pathways of the collapse of the helix-forming biopolymer polyalanine are investigated. To this end, the full time evolution of the helix-coil transition is simulated using molecular dynamics simulations. At the start of the transition short $3_{10}$-helices form, seemingly leading to the molecule becoming more aspherical midway through the collapse. After the completed collapse, the formation of $α$-helices seems to become the prevalent ordering mechanism leading to helical bundles, a structure representative for the equilibrium behavior of longer chains. The dynamics of this transition is explored in terms of the power-law scaling of two associated relaxation times as a function of the chain length.

cond-mat.soft↗

arXiv2025

Geometric Kolmogorov-Arnold Superposition Theorem

The Kolmogorov-Arnold Theorem (KAT), or more generally, the Kolmogorov Superposition Theorem (KST), establishes that any non-linear multivariate function can be exactly represented as a finite superposition of non-linear univariate functions. Unlike the universal approximation theorem, which provides only an approximate representation without guaranteeing a fixed network size, KST offers a theoretically exact decomposition. The Kolmogorov-Arnold Network (KAN) was introduced as a trainable model to implement KAT, and recent advancements have adapted KAN using concepts from modern neural networks. However, KAN struggles to effectively model physical systems that require inherent equivariance or invariance geometric symmetries as $E(3)$ transformations, a key property for many scientific and engineering applications. In this work, we propose a novel extension of KAT and KAN to incorporate equivariance and invariance over various group actions, including $O(n)$, $O(1,n)$, $S_n$, and general $GL$, enabling accurate and efficient modeling of these systems. Our approach provides a unified approach that bridges the gap between mathematical theory and practical architectures for physical systems, expanding the applicability of KAN to a broader class of problems. We provide experimental validation on molecular dynamical systems and particle physics.

cs.LG↗

arXiv2025

Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching

Long-range interactions are essential for the correct description of complex systems in many scientific fields. The price to pay for including them in the calculations, however, is a dramatic increase in the overall computational costs. Recently, deep graph networks have been employed as efficient, data-driven models for predicting properties of complex systems represented as graphs. These models rely on a message passing strategy that should, in principle, capture long-range information without explicitly modeling the corresponding interactions. In practice, most deep graph networks cannot really model long-range dependencies due to the intrinsic limitations of (synchronous) message passing, namely oversmoothing, oversquashing, and underreaching. This work proposes a general framework that learns to mitigate these limitations: within a variational inference framework, we endow message passing architectures with the ability to adapt their depth and filter messages along the way. With theoretical and empirical arguments, we show that this strategy better captures long-range interactions, by competing with the state of the art on five node and graph prediction datasets.

cs.LG↗

arXiv2025

Finite-Size Effects in Aging can be Interpreted as Sub-Aging

Systems brought out of equilibrium through a rapid quench from a disordered initial state into an ordered phase undergo physical aging in the form of phase-ordering kinetics, with characteristic dynamical scaling. In many systems, notably glasses, dynamical scaling is often described through sub-aging, where a phenomenological sub-aging exponent $0<μ< 1$ is empirically chosen to achieve the best possible data collapse. Here it is shown that finite-size effects modify the dynamical scaling behavior, away from simple aging with $μ=1$ towards $μ<1$, such that phenomenologically it would appear as sub-aging. This is exemplified for the exactly solved dynamical spherical model in dimensions $2<d<4$ and numerical simulations of the two-dimensional Ising model, with short-ranged and long-ranged interactions.

cond-mat.stat-mech↗

arXiv2024

Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passing

The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and first-principles methods at a fraction of their computational cost. The success of machine-learned interatomic potentials arises from integrating inductive biases such as equivariance to group actions on an atomic system, e.g., equivariance to rotations and reflections. In particular, the field has notably advanced with the emergence of equivariant message passing. Most of these models represent an atomic system using spherical tensors, tensor products of which require complicated numerical coefficients and can be computationally demanding. Cartesian tensors offer a promising alternative, though state-of-the-art methods lack flexibility in message-passing mechanisms, restricting their architectures and expressive power. This work explores higher-rank irreducible Cartesian tensors to address these limitations. We integrate irreducible Cartesian tensor products into message-passing neural networks and prove the equivariance and traceless property of the resulting layers. Through empirical evaluations on various benchmark data sets, we consistently observe on-par or better performance than that of state-of-the-art spherical and Cartesian models.

cs.LG↗

arXiv2024

Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials

Efficiently creating a concise but comprehensive data set for training machine-learned interatomic potentials (MLIPs) is an under-explored problem. Active learning, which uses biased or unbiased molecular dynamics (MD) to generate candidate pools, aims to address this objective. Existing biased and unbiased MD-simulation methods, however, are prone to miss either rare events or extrapolative regions -- areas of the configurational space where unreliable predictions are made. This work demonstrates that MD, when biased by the MLIP's energy uncertainty, simultaneously captures extrapolative regions and rare events, which is crucial for developing uniformly accurate MLIPs. Furthermore, exploiting automatic differentiation, we enhance bias-forces-driven MD with the concept of bias stress. We employ calibrated gradient-based uncertainties to yield MLIPs with similar or, sometimes, better accuracy than ensemble-based methods at a lower computational cost. Finally, we apply uncertainty-biased MD to alanine dipeptide and MIL-53(Al), generating MLIPs that represent both configurational spaces more accurately than models trained with conventional MD.

physics.comp-ph↗

arXiv2024

Non-universality of aging during phase separation of the two-dimensional long-range Ising model

We investigate the aging properties of phase-separation kinetics following quenches from $T=\infty$ to a finite temperature below $T_c$ of the paradigmatic two-dimensional conserved Ising model with power-law decaying long-range interactions $\sim r^{-(2 + σ)}$. Physical aging with a power-law decay of the two-time autocorrelation function $C(t,t_w)\sim \left(t/t_w\right)^{-λ/z}$ is observed, displaying a complex dependence of the autocorrelation exponent $λ$ on $σ$. A value of $λ=3.500(26)$ for the corresponding nearest-neighbor model (which is recovered as the $σ\rightarrow \infty$ limes) is determined. The values of $λ$ in the long-range regime ($σ< 1$) are all compatible with $λ\approx 4$. In between, a continuous crossover is visible for $1 \lesssim σ\lesssim 2$ with non-universal, $σ$-dependent values of $λ$. The performed Metropolis Monte Carlo simulations are primarily enabled by our novel algorithm for long-range interacting systems.

cond-mat.stat-mech↗

arXiv2024

Observations on Large-Scale Attenuation Effects in a 26 GHz Urban Micro-Cell Environment

This letter presents a measurement campaign carried out in an FR2 urban outdoor environment in a live experimental network deployment. The radio propagation analysis from a physical perspective at 26 GHz is essential for the correct deployment and dimensioning of future communication networks. This study performs a walk test emulating realistic conditions under which a pedestrian may be affected, summarizing and evaluating some of the typical effects encountered in a communications scenario such as penetration losses in a building, losses due to vegetation or the human body, or diffraction/scattering propagation around corners in street canyon-like environments. The operational conditions of the 5G network, the urban micro-cell scenario, and the use of omnidirectional antennas on the UE side validate the channel conditions from a perspective closer to a realistic scenario for a pedestrian within a FR2 live network.

eess.SP↗

arXiv2024

Temperature and Solvent Viscosity Tune the Intermediates During the Collapse of a Polymer

Dynamics of a polymer chain in solution gets significantly affected by the temperature and the frictional forces arising due to solvent viscosity. Here, using an explicit solvent framework for polymer simulation with the liberty to tune the solvent viscosity, we study the nonequilibrium dynamics of a flexible homopolymer when it is suddenly quenched from an extended coil state in good solvent to poor solvent conditions. Results from our extensive simulations reveal that depending on the temperature $T$ and solvent viscosity, one encounters long-lived sausage-like intermediates following the usual pearl-necklace intermediates. Use of shape factors of polymers allows us to disentangle these two distinct stages of the overall collapse process, and the corresponding relaxation times. The relaxation time $τ_s$ of the sausage stage, which is the rate-limiting stage of the overall collapse process, follows an anti-Arrhenius behavior in the high-$T$ limit, and the Arrhenius behavior in the low-$T$ limit. Furthermore, the variation of $τ_s$ with the solvent viscosity provides evidence of internal friction of the polymer, that modulates the overall collapse significantly, analogous to what is observed for relaxation rates of proteins during their folding. This suggests that the origin of internal friction in proteins is plausibly intrinsic to its polymeric backbone rather than other specifications.

cond-mat.soft↗