The DeepForce multiscale framework of Wu, Liang, Jeong, and Aluru (J. Chem. Phys. 159, 184108, 2023) links ab initio physics to continuum theory in one pipeline: a deep potential (DP) model trained on ab initio molecular dynamics (AIMD) data supplies atomic forces, a convolutional encoder–decoder network denoises the resulting force profiles, and the one-dimensional steady-state Nernst–Planck equation converts the smooth force profile into a density prediction for nanoconfined water — reproducing DPMD benchmark density profiles with relative error below 0.076 for graphene channels 1–6 nm wide, and predicting profiles at 8 and 20 nm, widths where AIMD and DPMD benchmarks are computationally out of reach, at a tiny fraction of the cost of AIMD. Its authors state that transferability to channel materials other than graphene and applicability to continuum theories beyond the Nernst–Planck equation have not been demonstrated, and that the training-data strategy for such extensions (fresh ab initio datasets versus transfer learning from the pre-trained models) is undecided. To date, the question remains open: the direct follow-up work from the same group still uses water in graphene slits with the Nernst–Planck equation, and no published work has demonstrated the DeepForce pipeline on a second channel material or coupled it to a second continuum theory.

Background

When water is confined in a nanochannel whose width is comparable to the molecular size, it forms oscillatory density layers (interfacial layering) near the walls, and the accuracy of any continuum-level prediction hinges on capturing the wall–water and water–water interactions at the quantum level. Ab initio molecular dynamics (AIMD — molecular dynamics driven by forces from density-functional theory, DFT) captures these quantum effects but is limited to a few hundred atoms and picosecond-scale trajectories, roughly channels up to ~1.5 nm. Machine-learned interatomic potentials, such as the deep potential (DP) model implemented in DeePMD-kit — a neural network trained to reproduce DFT energies and forces from local atomic environments — recover ab initio accuracy at much lower cost, but the resulting deep potential molecular dynamics (DPMD) is still bound to femtosecond time steps and becomes impractical for channels wider than a few nanometers.

To bypass explicit molecular dynamics entirely, Wu and Aluru earlier developed a deep-learning-based quasi-continuum theory (DL-QT, J. Chem. Phys. 157, 084121, 2022), in which a convolutional encoder–decoder (CED — an image-to-image neural network that maps a noisy discretized profile to a smooth one) infers the potential profile entering a continuum equation directly from thermodynamic conditions. The DeepForce framework (Wu, Liang, Jeong, Aluru, J. Chem. Phys. 159, 184108, 2023) upgraded this line to ab initio accuracy: (1) an AIMD library generated with VASP (the Vienna Ab initio Simulation Package, using the PBE exchange–correlation functional with D3 dispersion corrections — a standard DFT setup that includes van der Waals attraction) for water between parallel graphene sheets, in single-surface and bulk-water geometries, at 18 channel widths from 5 Å to 40 Å; (2) a DP model trained on this library to generate forces; (3) a CED denoising network mapping noisy DP force profiles to the smooth profiles defined by 1-nanosecond DPMD averages; and (4) the one-dimensional steady-state Nernst–Planck equation

ddx ⁣(dρdx−ρRT f(x))=0,\frac{d}{dx}\!\left(\frac{d\rho}{dx}-\frac{\rho}{RT}\,f(x)\right)=0,

where ρ(x)\rho(x) is the center-of-mass density profile across the channel, f(x)f(x) is the total fluid force per unit mole (wall–fluid plus fluid–fluid), RR the gas constant, and TT the temperature. Fed with the denoised force, this continuum solver reproduces DPMD benchmark density profiles with relative error below 0.076 for channel widths from 1 to 6 nm, and predicts profiles at 8 and 20 nm where AIMD/DPMD benchmarks are computationally out of reach. A by-product of the study is a quantified warning that classical MD with the SPC/E water model (a standard classical fixed-point-charge model of water) and standard graphene–water Lennard-Jones parameters errs by more than 25% in relative density error for channels below 4 nm, including qualitatively wrong layering.

Two structural limitations of this demonstration frame the open question. First, all training data describe water confined between graphene sheets; other technologically relevant channel materials (for example hexagonal boron nitride or molybdenum disulfide, whose different surface chemistry, polarization, and electronic structure change the wall–water interaction) are absent. Second, the Nernst–Planck step is an equilibrium, one-dimensional, structure-only closure: it delivers the density profile ρ(x)\rho(x) but not transport, flow, or thermodynamic response. Extending the pipeline to other materials demands either new ab initio datasets or transfer learning — fine-tuning the pre-trained DP and CED models on a small amount of new-material data — and the 2023 paper explicitly notes both routes without deciding between them. Related literature has evaluated DP-model transferability for the water–graphene system itself (Liu, Wu, and Lu, J. Chem. Phys. 159, 044712, 2023, using DP-GEN, a concurrent-learning algorithm that iteratively adds training configurations wherever the current model is least accurate) and has demonstrated transfer learning for the adjacent problem of coarse-graining simple liquids in confinement (Nadkarni, Wu, and Aluru, J. Chem. Theor. Comput. 19, 7358, 2023), but neither addresses the coupled ab-initio-to-continuum pipeline. In parallel, Bui and Cox (Proc. Natl. Acad. Sci. U.S.A., 2026) combined machine-learned interatomic potentials with neural classical density functional theory (cDFT — a continuum theory that obtains inhomogeneous density profiles by minimizing a free-energy functional) to predict confinement-modified liquid–vapor coexistence of water between fitted 9-3 Lennard-Jones walls (an analytic wall–fluid potential obtained by integrating Lennard-Jones interactions over a solid half-space), showing that a non-Nernst–Planck continuum closure can be coupled to ab initio-trained models; however, that framework represents the walls by an implicit fitted potential rather than AIMD wall–fluid physics, is restricted to planar geometries and equilibrium structure/thermodynamics, and does not build on or extend the DeepForce pipeline.

Problem Statement

Extend the DeepForce ab-initio-to-continuum pipeline — ab initio molecular dynamics data, a deep potential force model, neural denoising of force profiles, and a continuum solver — beyond the single demonstrated system of water confined between graphene sheets. As posed by the source paper, the undemonstrated extensions are: (1) transferability to channel materials other than graphene, i.e. demonstrating that the pipeline (retrained or adapted) predicts ab-initio-accuracy density profiles for water in nanochannels of a genuinely different wall material such as hexagonal boron nitride or molybdenum disulfide, whose wall–water interactions differ in polarization and surface chemistry; and (2) applicability to continuum theories beyond the one-dimensional steady-state Nernst–Planck equation, i.e. coupling the deep-learned force information to a continuum closure that captures physics the Nernst–Planck equation cannot, such as transport/flow or equilibrium thermodynamic response. Resolution requires a demonstrated, validated extension of the pipeline beyond the single water/graphene/one-dimensional-steady-state-Nernst–Planck setting in at least one of these two source-stated directions — ab-initio-accuracy density profiles for water in a nanochannel of at least one genuinely different wall material, or a coupling of the deep-learned force information to a continuum closure beyond the Nernst–Planck equation that captures additional physics (and, for that extension, the additional observable the chosen theory provides) — with accuracy assessed against ab initio or deep potential molecular dynamics (DPMD) benchmarks as in the source paper. A demonstration in one direction resolves that direction's stated limitation; the other direction remains open. The source paper also notes two possible training-data strategies for such extensions — fresh ab initio datasets versus transfer learning from the pre-trained models — without deciding between them; settling this choice is an open methodological sub-question, not a condition for resolving either extension.

References

  1. Haiyi Wu, Chenxing Liang, Jinu Jeong, and N. R. Aluru, 'From ab initio to continuum: Linking multiple scales using deep-learned forces', The Journal of Chemical Physics 159, 184108 (2023). DOI: 10.1063/5.0166927, https://doi.org/10.1063/5.0166927
  2. Haiyi Wu and N. R. Aluru, 'Deep learning-based quasi-continuum theory for structure of confined fluids', The Journal of Chemical Physics 157, 084121 (2022). DOI: 10.1063/5.0096481, https://doi.org/10.1063/5.0096481
  3. Bugra Yalcin, Ishan Nadkarni, Jinu Jeong, Chenxing Liang, and Narayana R. Aluru, 'Generative Quasi-Continuum Modeling of Confined Fluids at the Nanoscale', arXiv:2509.08223 (2025). DOI: 10.48550/arXiv.2509.08223, https://arxiv.org/abs/2509.08223
  4. Anna T. Bui and Stephen J. Cox, 'A unified machine-learning framework for ab initio multiscale modeling of liquids', Proceedings of the National Academy of Sciences 123, e2610049123 (2026). DOI: 10.1073/pnas.2610049123, https://doi.org/10.1073/pnas.2610049123 (preprint arXiv:2603.20493, https://arxiv.org/abs/2603.20493)
  5. Yuanhao Li, 'How Machine Learning Predicts Fluid Densities under Nanoconfinement', arXiv:2508.17732 (2025); published as 'Fluid density regulation under nanoconfinement revealed by machine learning', Physical Chemistry Chemical Physics 28, 6200–6207 (2026). DOI: 10.1039/d5cp03804a, https://doi.org/10.1039/d5cp03804a
  6. Dongfei Liu, Jianzhong Wu, and Diannan Lu, 'Transferability evaluation of the deep potential model for simulating water-graphene confined system', The Journal of Chemical Physics 159, 044712 (2023). DOI: 10.1063/5.0153196, https://doi.org/10.1063/5.0153196
  7. Ishan Nadkarni, Haiyi Wu, and N. R. Aluru, 'Data-Driven Approach to Coarse-Graining Simple Liquids in Confinement', Journal of Chemical Theory and Computation 19, 7358–7370 (2023). DOI: 10.1021/acs.jctc.3c00633, https://doi.org/10.1021/acs.jctc.3c00633
  8. Zhongwu Li and Aleksandr Noy, 'Carbon nanotube nanofluidics', Chemical Society Reviews 54, 8582–8635 (2025). DOI: 10.1039/d5cs00233h, https://doi.org/10.1039/d5cs00233h
  9. Baochao Shan, Shaokang Li, Guihua Tang, Manuel Torrilhon, Yonghao Zhang, and Zhaoli Guo, 'Molecular kinetic modelling of confined fluid transport—a mesoscopic approach', Acta Mechanica Sinica 42, 724893 (2026). DOI: 10.1007/s10409-025-24893-x, https://doi.org/10.1007/s10409-025-24893-x
  10. Zhonglin Cao, Yuyang Wang, Cooper Lorsung, and Amir Barati Farimani, 'Neural Network Predicts Ion Concentration Profiles under Nanoconfinement', The Journal of Chemical Physics 159, 094702 (2023). DOI: 10.1063/5.0147119, https://doi.org/10.1063/5.0147119