Unified framework for machine learning interatomic potentials.
problem Designing and optimizing machine learning models for interatomic potentials.
method Unified mathematical framework unifying ACE and NequIP, providing a systematic design space.
result Demonstrated through ablation studies, critical design choices for high accuracy.
Improved neural network models predict molecular and material properties efficiently.
problem Training neural networks for accurate interatomic potentials is computationally expensive.
method Gaussian moment-based neural networks with improved architecture and active learning.
result The new models achieve high accuracy and reduced training times.
Transfer learning boosts chemically accurate neural network potentials for organic molecules.
problem Developing accurate interatomic potentials from ab-initio data.
method Discriminative fine-tuning of pre-trained neural networks.
result Fine-tuning with energy labels alone can achieve accurate atomic forces.
Paper proposes new methods for improving interatomic potentials.
problem Limitations of conventional SO(2) Linear architectures in MLIPs.
method Direct Cartesian construction, recursive Clebsch-Gordan construction, Edge Complex Product Basis, Radial Rotary Complex Attention.
result TECE-OAM-RRA-1.0 achieves SOTA performance on Matbench Discovery.
HAL accelerates the generation of training sets for accurate interatomic potentials.
problem Generating accurate and transferable interatomic potentials is time-consuming and requires expert input.
method HAL framework using a physically motivated sampler with a biasing term to drive high uncertainty configurations.
result HAL-generated training databases for alloys and polymers predict macroscopic properties with high accuracy.
A new training method improves MLIPs for faster, lighter simulations.
problem High computational and memory costs of complex MLIPs for large-scale MD simulations.
method Teacher-student training framework using latent atomic energy knowledge.
result Lightweight student MLIPs achieve faster MD speeds and comparable accuracy to teachers.
New method uses biased MD to create accurate MLIPs.
problem Creating a comprehensive data set for MLIPs.
method Bias MD by MLIP's energy uncertainty, using gradient-based uncertainties.
result Develops uniformly accurate MLIPs with lower computational cost.
A universal interatomic potential for an arbitrary set of chemical elements is urgently needed in computational materials science. Graph convolution neural network (GCN) has rich expressive power, but previously was mainly employed to transport scalars and vectors, not rank ≥2 tensors. As classic interatomic poten…
Automatically detects and down-weights noisy samples in machine learning training.
problem Numerical noise in reference data hampers the accuracy of machine learning models.
method On-the-fly outlier detection using exponential moving average to identify and down-weight noisy samples.
result The method prevents overfitting and matches the performance of iterative refinement with reduced overhead.
Unconstrained MLIPs outperform constrained ones in accuracy and speed.
problem Improving the efficiency and accuracy of machine-learned interatomic potentials.
method Investigated unconstrained models trained on large datasets compared to physically constrained models.
result Unconstrained MLIPs can be superior in accuracy and speed compared to physically constrained models.
Committee neural network models improve accuracy and enable active learning for interatomic potentials.
problem Improving accuracy and generalization error in interatomic potentials.
method Adapting committee models to neural networks, using multiple models with shared descriptors, and applying active learning to select configurations.
result Committee disagreement provides a measure of generalization error and guides active learning to minimize it.
Optimized GPRNN reduces model complexity and overfitting, improving performance.
problem Overfitting in neural networks and high model complexity.
method Gaussian Process Regression - Neural Network hybrid with optimized redundant coordinates.
result Optimized GPRNN achieves lower test set error with fewer terms/neurons.
DenSNet learns electron densities for molecular dynamics, enabling accurate spectroscopic predictions.
problem Lack of accurate electronic observables in MLIPs for molecular dynamics.
method DenSNet uses SE(3)-equivariant neural networks to predict electron densities and total energy.
result DenSNet predicts infrared spectra with excellent agreement to experimental data.
Machine learning models accurately predict molecular magnetic anisotropy tensors.
problem Accurately modeling molecular magnetic anisotropy tensors.
method Gaussian-moment neural-network approach for machine learning.
result Achieved accuracy of 0.3--0.4 cm−1 for magnetic anisotropy tensor predictions. Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the computationally expensive density functional theory calculations. Combining many-bod…
Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be the first choice for images, audio and video data, the atoms in molecules are not …
Enhances diffusion-based sampling for molecular systems.
problem Inefficiency and thermodynamic mode miss in diffusion-based samplers for molecular systems.
method Introduces a sequential bias along collective variables (CVs) to encourage exploration and increase temperature in the projected space.
result Improves efficiency, mode discovery, and free energy estimation; first to demonstrate reactive sampling.
Data-driven prediction of molecular properties presents unique challenges to the design of machine learning methods concerning data structure/dimensionality, symmetry adaption, and confidence management. In this paper, we present a kernel-based pipeline that can learn and predict the atomization energy of molecules wit…
In this article we discuss the distribution of asset price movements by the market potential function. From the principle of free energy minimization we analyze two different kinds of market potentials. We obtain a U-shaped potential when market reversion (i.e. contrarian investors) is dominant. On the other hand, if t…
Develops potential theory for WZW equation in Kähler potentials space.
problem Solving the Wess--Zumino--Witten equation in Kähler potentials.
method Introduces ω-harmonicity on graphs to characterize the WZW equation and uses subharmonic distance. result Shows solvability of Dirichlet problem and approximation by finite-dimensional maps.
The paper examines stability of harmonic and symphonic maps with forms and potentials.
problem Stability of harmonic and symphonic maps with forms and potentials.
method Analyzes stability of F-harmonic and F-symphonic maps with forms and potentials. result Stability conditions for harmonic and symphonic maps are established.
The paper examines stability of subelliptic harmonic maps with potential.
problem Stability of subelliptic harmonic maps with potential.
method Derived first and second variation formulas, proved stability conditions, and gave instability results.
result Subelliptic harmonic maps with potential are stable under certain curvature and potential conditions.
The paper describes flat Hessian metrics on surfaces and their potentials.
problem Understanding Hessian metrics on surfaces.
method Theoretical description and explicit construction using integrable systems.
result Explicit construction of potentials for flat Hessian metrics on surfaces.
A hyperKähler potential is a function rho that is a Kähler potential for each complex structure compatible with the hyperKähler structure. Nilpotent orbits in a complex simple Lie algebra are known to carry hyperKähler metrics admitting such potentials. In this paper, we explicitly calculate the hyperKähler potential w…
We consider the problem of learning an interpretable potential energy function from a Hamiltonian system's trajectories. We address this problem for classical, separable Hamiltonian systems. Our approach first constructs a neural network model of the potential and then applies an equation discovery technique to extract…
Article provides Bernstein gradient estimates for heat equations with potential terms.
problem Gradient estimates for heat equations with potential terms on weighted Riemannian manifolds.
method Derived Bernstein type gradient estimates for two systems of heat equations with linear, exponential, and combined potentials.
result Resolves part of the problem raised by Bhattacharyya et al. in \cite{SB-1}.
In this paper we study potential function of gradient steady Ricci solitons. We prove that infimum of potential function decays linearly; in particular, potential function of rectifiable gradient steady Ricci solitons decays linearly. As a consequence, we show that a gradient steady Ricci soliton with bounded potential…
We consider the geodesic equation for the generalized Kahler potential with only mixed second derivatives bounded. We show that given such two generalized Kahler potentials, there is a unique geodesic segment such that for each point on the geodesic, the generalized Kahler potential has uniformly bounded mixed second d…
We show two results about the Conway potential function which is known as the normalized multivariable Alexander polynomial. We first show that the Conway potential function introduced by Kauffman in "Formal Knot Theory" is indeed a link invariant. Next we show that Kauffman's potential function equals Hartley's potent…
The paper characterizes potential functions whose level sets are orbits in mechanical systems.
problem Characterizing smooth potential energy functions on the plane with specific level set properties.
method Analyzing inverse curvature flow and properties of level sets.
result Analytic or functions with totally path-disconnected critical sets must be radial, while every compact convex set is a critical set of a Levi potential.
The paper studies m-quasi Einstein manifolds with convex potential and finds constant scalar curvature.
problem Investigating m-quasi Einstein manifolds with a convex potential function. method Analyzing integral conditions and properties of the potential vector field.
result An m-quasi Einstein manifold with a convex potential function has constant scalar curvature. Estimates classical potential from stock price data using quantum mechanics.
problem Estimating classical potential from empirical stock price data.
method Quantum mechanical model of stock price distribution, estimating potential from wave function.
result Suggests methods to evaluate classical potential for Schrodinger equation.
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The results here can be applied to the double well potential.
New proof of Penrose inequality using potential theory.
problem Proving the Riemannian Penrose inequality for black holes.
method Establishing a monotonicity formula for the p-capacitary potential.
result A new proof of the Penrose inequality for black holes.
Paper connects AJ conjecture and colored Jones polynomial potential function.
problem Relationship between A-polynomial and colored Jones polynomial. method Connects AJ conjecture and colored Jones polynomial potential function.
result Establishes connection between A-polynomial and colored Jones polynomial potential function. It is known that nilpotent orbits in a complex simple Lie algebra admit hyperKähler metrics with a single function that is a global potential for each of the Kähler structures (a hyperKähler potential). In an earlier paper the authors showed that nilpotent orbits in classical Lie algebras can be constructed as finite-d…
We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated…
New method constructs potential functions for Kähler-Einstein metrics.
problem Constructing potential functions for Kähler-Einstein metrics on pseudoconvex domains.
method Method of potential scaling.
result Existence of 1-parameter family of automorphisms for certain pseudoconvex domains.
New proof shows compact homogeneous LCK manifolds are Vaisman.
problem Proving compact homogeneous LCK manifolds are Vaisman.
method Using homogeneous LCK manifolds with potential and a new metric construction.
result Compact homogeneous LCK manifolds are Vaisman.
Study classifies static potentials on 3-manifolds, proving one-dimensionality under specific conditions.
problem Classifying the dimension of static potentials on 3-manifolds.
method Analysis of relative zero sets of static potentials, using Miao and Tam's technique.
result Proves one-dimensionality of static potentials under specific conditions.
New proof and insights on Elliptical Potential Lemma for online learning.
problem Limitations in the original proof of the Elliptical Potential Lemma.
method Proposes a new proof and new perspectives on the lemma.
result New flexibility in the type of potentials considered.
Study magnetic geodesics on Kähler potentials using variational methods.
problem Understanding magnetic geodesics on Kähler potentials.
method Variational method for a generalized Landau-Hall functional.
result Magnetic geodesic equation and its relation to a perturbed complex Monge-Ampère equation.
Study of metrics on positive-definite matrices from power potential, linking to power means.
problem Understanding metrics on positive-definite matrices derived from power potential.
method Explicit expressions for geodesics and distance function derived from Hessian of power potential.
result Geodesics and distance function converge to weighted matrix geometric mean as β tends to zero.
Extends potential theory to Carnot groups, estimating Hausdorff dimension.
problem Estimating Hausdorff dimension of polar sets in Carnot groups.
method Geometric completeness and Riesz potential inequalities in Carnot groups.
result Developed applications in CR geometry and quaternionic CR geometry.
New theorem on Lee classes for LCK manifolds with potential.
problem Determining Lee classes on LCK manifolds with potential.
method Analyzing cohomology classes of Lee forms and proving the result for Vaisman manifolds.
result The set of Lee classes on LCK manifolds with potential forms an open half-space in H1(M,R). We study the influence of an additional scalar potential on various geometric and analytic properties of Dirac-harmonic maps. We will create a mathematical wish list of the possible benefits from inducing the potential term and point out that the latter cannot be achieved in general. Finally, we focus on several potent…
PO-Flow models potential and counterfactual outcomes for personalized treatment decisions.
problem Predicting individualized treatment effects from observational data.
method Continuous normalizing flow (CNF) framework for causal inference.
result Unified approach to potential outcome prediction, treatment effect estimation, and counterfactual prediction.
The development of accurate and transferable machine learning (ML) potentials for predicting molecular energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the gene…