SurfDesign: Surface-First Design Paradigms

• SurfDesign is a surface-centered design paradigm that treats surfaces as primary objects for optimization, synthesis, and simulation across diverse fields.
• It replaces indirect proxies with explicit representations such as molecular point clouds, signed distance functions, and geodesics to improve design accuracy.
• Applications span protein design, fluid inverse design, coastal wave modeling, surfactant generation, and interactive CAD on manifold meshes.

Searching arXiv for papers directly relevant to “SurfDesign” and adjacent uses of the term. {"query":"SurfDesign arXiv SurfDesign surfaces design protein fluid surf zone surfactant", "max_results": 10} I found several relevant arXiv entries connected to the term “SurfDesign” or to surface-centered design paradigms, including the core protein-design paper “SurfDesign: Effective Protein Design on Molecular Surfaces” (Wu et al., 25 May 2026), the fluid/surface inverse-design framework “SURFSUP: Learning Fluid Simulation for Novel Surfaces” (Mani et al., 2023), and related surface-manifold tooling such as “B/Surf: Interactive Bézier Splines on Surfaces” (Mancinelli et al., 2021). For rough-bottom surf-zone modeling, the related wave-transformation work (Ancilotti et al., 26 Mar 2025) is also relevant where “SurfDesign” is used in a coastal-engineering sense. SurfDesign is a surface-centered design paradigm in which surfaces are treated as the primary conditioning object for synthesis, simulation, or optimization. In current arXiv usage, the term is most explicitly associated with molecular-surface-conditioned protein design, but closely related surface-first formulations also appear in inverse design of fluid-manipulating objects, rough-bottom surf-zone modeling, non-ionic surfactant generation, and interactive spline construction on manifold meshes (Wu et al., 25 May 2026, Mani et al., 2023, Ancilotti et al., 26 Mar 2025, Sheikh et al., 29 Nov 2025, Mancinelli et al., 2021). Across these settings, the common technical move is to replace indirect proxies with explicit surface representations: oriented molecular point clouds, signed distance functions, roughness influence layers, or intrinsic mesh geodesics.

1. Surface-first design as a unifying idea

A concise way to organize current usage is by the representation chosen for the surface-bearing object and the optimization or generation task built on top of it.

Domain	Primary representation	Design or modeling target
Protein design	Molecular surface $Q=\{(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)\}$	Sequence design conditioned on surface geometry and physicochemical features
Fluid-object design	Signed distance function $F(p;\phi)$	Gradient-based inverse design of bowls, funnels, and latent shapes
Surf-zone modeling	Roughness influence layer and Bulk Canopy Drag	Phase-resolved wave transformation over rough rocky bottoms
Surfactant design	SMILES and 2D molecular graphs	Conditional generation for pCMC, AW_ST_CMC, and Area_min
Manifold graphics	Manifold triangle mesh with geodesic averages	Interactive Bézier spline drawing and editing on surfaces

In the protein-design setting, SurfDesign is explicitly formulated as learning $$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$ and maximizing $\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$. In the fluid-design setting, the corresponding object is a differentiable simulator $f_\theta:(X^{(t)},F)\to Y^{(t)}$ whose geometry enters through SDF queries. In rocky surf-zone modeling, the surface acts through a volumetric drag parameterization rather than an explicit triangulated interface, while in manifold graphics the surface is the domain on which design curves are intrinsically defined. This suggests that current usage of “SurfDesign” is best understood as a family of surface-conditioned methods rather than a single software stack.

2. Molecular-surface-conditioned protein design

The most direct use of the name is "SurfDesign: Effective Protein Design on Molecular Surfaces" (Wu et al., 25 May 2026). The framework replaces backbone-only conditioning with conditioning on a molecular surface $Q=\{q_i\}_{i=1}^m$, where $q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$ contains surface coordinates, unit normals, and physicochemical features. Surface points are generated from SAS and SES using PyMOL, and $\mathbf{h}_i$ is computed from local atomic geometry and atom types only; following MaSIF, the feature set includes Poisson–Boltzmann electrostatics, hydrophobicity, and free electrons/protons, with the retained ablation indicating hydrophobicity and charge as most important. A $k$-NN graph $\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$ is built on the surface, and Gaussian kernel smoothing is applied to coordinates.

The geometry encoder treats the molecular surface as a smooth manifold embedded in $F(p;\phi)$0. Local shape is summarized by a covariance matrix

$F(p;\phi)$1

with eigenvalues $F(p;\phi)$2 normalized into pseudo-curvatures $F(p;\phi)$3. Pairwise directional geometry is encoded by angles $F(p;\phi)$4, $F(p;\phi)$5, and the dihedral $F(p;\phi)$6, then expanded with spherical Fourier–Bessel bases. These invariant quantities feed the SE(3)-equivariant surface message passing encoder. At layer $F(p;\phi)$7, messages are built from node features, curvature descriptors, radial bases, and SFB encodings, reweighted by attention, and used to update both scalar features and coordinates: $F(p;\phi)$8

$F(p;\phi)$9

Normals and pseudo-curvatures are recomputed after each coordinate update by local covariance eigendecomposition, with the smallest-eigenvalue eigenvector used as the updated normal.

Surface features are injected into ESM-2 through a parameter-efficient fine-tuning scheme combining structural adapters with LoRA. For a weight $$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$0, the LoRA update is

$$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$1

with rank $$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$2 and scaling $$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$3. Training follows conditional masked language modeling: $$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$4 optimized by cross-entropy over masked residues.

Functionally, SurfDesign consistently outperforms the compared surface-conditioned and backbone-only baselines on the reported benchmarks. In de novo binder design across six targets, it attains the best average AF2 pAE$$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$5, 15.85 versus 16.95 for SurfPro, and the highest weighted-average success rate, 30.14% versus 26.22% for SurfPro-Pretrain. In enzyme design, it reports the best average ESP success rate, 47.30% versus 42.23% for SurfPro and 43.63% for SurfPro-Pretrain. On inverse-folding benchmarks used as structural-compatibility diagnostics, it reaches PPL 2.41 and AAR 74.13% on CATH 4.2, and on TS50/TS500 it reports AAR up to 83.44% and 85.12%, respectively. The paper explicitly emphasizes that inverse-folding metrics such as AAR and perplexity are diagnostics of structural compatibility rather than the primary functional objective (Wu et al., 25 May 2026).

3. Fluid-mechanical inverse design of novel surfaces

A second, explicitly design-oriented use of the term arises from the SURFSUP framework, where surface design is implemented through a learned particle-based fluid simulator conditioned on signed distance functions rather than explicit surface particles or meshes (Mani et al., 2023). The fluid state at time $$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$6 is represented by particles

$$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$7

and a rigid surface $$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$8 is encoded by an SDF $$\mathcal{F}_\vartheta:\mathcal{Q}\rightarrow\mathcal{S}$$9. The learned forward model

$\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$0

predicts per-particle accelerations $\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$1, followed by Euler integration

$\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$2

The SDF representation provides distance and approximate outward normal information through $\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$3 and $\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$4, with $\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$5 outside the solid, $\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$6 inside, and $\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$7 on the zero level set. Surfaces are encoded directly in node features,

$\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$8

inside a GNS-style encode–process–decode architecture with radius-based edges and $\log p(\mathcal{S}\mid \mathcal{Q};\vartheta)$9 message-passing steps. The model is trained against SPlisHSPlasH with a near-surface weighted loss

$f_\theta:(X^{(t)},F)\to Y^{(t)}$0

where $f_\theta:(X^{(t)},F)\to Y^{(t)}$1. The training domain, PrimShapes, contains 1000 training simulations of water falling onto spheres, boxes, cylinders, cones, and toruses in a $f_\theta:(X^{(t)},F)\to Y^{(t)}$2 m container, each rollout lasting 800 steps at $f_\theta:(X^{(t)},F)\to Y^{(t)}$3.

The central design result is differentiability with respect to geometry parameters $f_\theta:(X^{(t)},F)\to Y^{(t)}$4, whether analytic primitive parameters, CSG parameters, or neural SDF latent codes. Because the pipeline

$f_\theta:(X^{(t)},F)\to Y^{(t)}$5

is differentiable, scalar objectives $f_\theta:(X^{(t)},F)\to Y^{(t)}$6 can be optimized by reverse-mode autograd. The paper demonstrates this on bowl and funnel design with $f_\theta:(X^{(t)},F)\to Y^{(t)}$7, where $f_\theta:(X^{(t)},F)\to Y^{(t)}$8 is a capture radius and $f_\theta:(X^{(t)},F)\to Y^{(t)}$9 a filter radius. Bowl optimization maximizes a 3D Gaussian log-probability of final particle positions near a bottom interior target; funnel optimization maximizes a 2D Gaussian log-probability of ground-contact particles near a target point. Rollout horizons are 50 steps for the bowl and 75 for the funnel. The same framework is extended to DeepSDF latent-space optimization of a “wet” chair, where a chair latent $Q=\{q_i\}_{i=1}^m$0 is optimized for $Q=\{q_i\}_{i=1}^m$1 steps to create a concave seat/back region that traps water.

Generalization to novel surfaces is quantitatively strong. On Primitives-OOD, SURFSUP reports Chamfer Surface 10.95 versus 18.45 for the GNS baseline, Inside particles 324 versus 33,006, and Mean SDF inside approximately $Q=\{q_i\}_{i=1}^m$2 versus $Q=\{q_i\}_{i=1}^m$3. On Funnels, the corresponding Inside particles are 2 versus 7204. On Complex-Scenes, SURFSUP reports Chamfer Surface 50.52 versus 276.18 and Inside particles 40,513 versus 257,722. The paper also stresses a computational advantage: the baseline uses approximately 2000 surface particles plus approximately 2000 fluid particles, whereas SURFSUP uses only fluid particles plus SDF queries. This makes the framework particularly suitable for repeated optimization loops, although the reported inverse-design experiments are low-dimensional and the work does not provide an explicit analysis of vanishing or exploding gradients over longer horizons (Mani et al., 2023).

4. Coastal-engineering uses: surf-zone transformation over rough bottoms

In coastal hydrodynamics, SurfDesign appears as the notion of a high-fidelity surf-zone design or hazard-assessment tool whose accuracy depends on explicit roughness-aware wave modeling (Ancilotti et al., 26 Mar 2025). The relevant paper adapts Bulk Canopy Drag into the 3D non-hydrostatic SYMPHONIE model to represent wave dissipation over rough rocky seabeds. The governing framework is incompressible Navier–Stokes with Boussinesq approximation and hydrostatic/non-hydrostatic pressure splitting, with the added volume force

$Q=\{q_i\}_{i=1}^m$4

Here $Q=\{q_i\}_{i=1}^m$5 is the turbulent drag coefficient, $Q=\{q_i\}_{i=1}^m$6 the laminar coefficient, and $Q=\{q_i\}_{i=1}^m$7 the inertial or added-mass coefficient. The study works in a phase-resolved setting with a piston wavemaker forcing a JONSWAP irregular wave with $Q=\{q_i\}_{i=1}^m$8 and $Q=\{q_i\}_{i=1}^m$9, using an 8 m by 0.15 m numerical flume, $q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$0, 10 sigma layers, and $q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$1.

A key modeling step is the replacement of a thin bottom shear-stress formulation by a volumetric drag layer of height

$q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$2

derived from the standard deviation of bed elevation over the rough region. Dimensionless regime selection follows

$q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$3

For the LEGOLAS rough-ramp experiment, the authors retain turbulent and inertial drag and set the laminar term effectively to zero. Three rough-bed configurations are tested: turbulent only $q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$4, inertial only $q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$5, and combined $q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$6, with $q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$7 in all cases.

Validation is performed against the LEGOLAS laboratory data. The smooth-bed case, calibrated with breaking only and BCD off, yields RMSE $q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$8 m and WI $q_i=(\mathbf{x}_i,\mathbf{n}_i,\mathbf{h}_i)$9. For the rough bed, turbulent drag only gives RMSE $\mathbf{h}_i$0 m and WI $\mathbf{h}_i$1; inertial drag only gives RMSE $\mathbf{h}_i$2 m and WI $\mathbf{h}_i$3; and the combined configuration gives the best agreement, RMSE $\mathbf{h}_i$4 m and WI $\mathbf{h}_i$5. The physical interpretation reported in the paper is that turbulent drag dominates the outer surf zone, while inertial drag plays a key role in the inner surf zone. The same paper explicitly recommends that a SurfDesign-type coastal tool should apply BCD volumetrically through the roughness layer, determine $\mathbf{h}_i$6 from bathymetric statistics such as $\mathbf{h}_i$7, and calibrate $\mathbf{h}_i$8 and $\mathbf{h}_i$9 against local $k$0, $k$1, and topographic descriptors rather than treat them as universal constants (Ancilotti et al., 26 Mar 2025).

5. Digital surfactant design as a “SurfDesign stack”

The paper "Digital Surfactant" states that it can be read as a compact “SurfDesign” stack for non-ionic surfactants (Sheikh et al., 29 Nov 2025). Its pipeline comprises a data layer built on SurfPro, predictive GNNs, two complementary generative models, and DFT/MD validation. The design space is restricted to non-ionic and sugar-based non-ionic surfactants, represented as SMILES and 2D graphs, and conditioned on three target properties: $k$2, $k$3, and $k$4. SurfPro contains 1624 molecules across 8 types, but only 647 have all six experimental properties recorded; this paper uses 425 non-ionic molecules in total, with the remainder of the missing values imputed from AttentiveFP ensembles following Hödl et al. The generative training set for non-ionics contains 388 molecules, and 37 test molecules provide target conditions.

The first generator is GraphDiT, a discrete diffusion model over unified graph features $k$5, trained in single-property and multi-property modes. The forward noising process is

$k$6

with classifier-free guidance at generation time,

$k$7

The second generator is an encoder–decoder transformer trained on matched molecular pairs $k$8, where $k$9 is discretized as property-change tokens such as $\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$0pCMC bins prepended to the input. Pretraining uses 198,560 ChEMBL MMPs, and finetuning uses 1267 SurfPro-derived MMPs. Property prediction is handled by AttentiveFP models with approximately 116k learnable parameters, trained with AdamW and Huber loss. On the SurfPro test set, the multi-property predictor reports MAE/RMSE/$\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$1 of 0.251/0.372/0.879 for pCMC, 2.514/3.508/0.810 for AW_ST_CMC, and 0.209/0.322/0.764 for Area_min.

Generation results expose a clear exploration–exploitation trade-off. Diff-Single reports 96.757% validity, 0.836 diversity, Dist 6.457, coverage 7/7, and pCMC MAE 0.975; Trfm-Single reports 96.429% validity, 0.661 diversity, Dist 7.401, coverage 4/7, and pCMC MAE 0.482. In the multi-property setting, Diff-Multi reports 96.757% validity, 0.840 diversity, Dist 5.260, and MAEs 1.306, 4.039, and 0.286 for pCMC, AW_ST_CMC, and Area_min; Trfm-Multi reports 100% validity, 0.640 diversity, Dist 7.662, and MAEs 0.695, 2.938, and 0.150. The paper’s interpretation is explicit: the inverse design model is better at generating a diverse set of molecules, while the transformer is better at generating molecules that satisfy input property constraints better, and single-property conditioning satisfies the target property better on average than multi-property conditioning.

Screening uses normalized deviation

$\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$2

and, in the multi-property case,

$\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$3

Eight screened molecules are then validated by DFT and MD. Geometry optimization is performed with B3LYP/6-311++G* and frequency analysis confirms true minima. Interfacial behavior is simulated in GROMACS using slab geometries, with surface tension computed from the pressure tensor as

$\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$4

Most predicted pCMC and AW_ST_CMC values are reported as close to the simulated results, with one notable outlier for Diff-Multi candidate 2, where predicted AW_ST_CMC is 29.27 and simulated AW_ST_CMC is 45.42. The broader implication stated in the paper is that a reusable SurfDesign stack can combine a generative exploration model, a local optimization model, property predictors, and MD-based validation in a closed digital-design loop (Sheikh et al., 29 Nov 2025).

6. Geometric and numerical foundations: manifold curves, weakly dispersive waves, and SPH

A broader technical substrate for SurfDesign is supplied by methods that make surface geometry directly computable or editable. "B/Surf: Interactive Bézier Splines on Surfaces" defines Bézier curves intrinsically on manifold triangle meshes using repeated geodesic pairwise averages $\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$5, where $\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$6 is a shortest geodesic between $\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$7 and $\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$8 (Mancinelli et al., 2021). Direct manifold extensions of De Casteljau and Bernstein evaluation are shown to be fragile because cut-locus events can cause discontinuities when control polygons become large. The robust alternatives are subdivision-based: Recursive De Casteljau bisection, whose limit curve is $\mathcal{G}_Q=(\mathcal{V}_Q,\mathcal{E}_Q)$9, and the open-uniform Lane–Riesenfeld scheme, whose limit curve is $F(p;\phi)$00 on the interior. The system supports curve tracing, point evaluation, point insertion, all standard anchor/handle interactions of 2D tools, and mapping complex SVG drawings to the mesh. Robustness is tested on all 5,567 watertight manifold models in Thingi10k, with 556,700 random cubic control polygons and no preprocessing; more than 98–99% of traces complete in under 0.1 s, and all algorithms produce valid curves in all trials. For surface-centric CAD-like workflows, this supplies an intrinsic curve primitive for editing directly on manifold geometry rather than in a parameterization.

For nearshore wave design, "Fully nonlinear weakly dispersive modelling of wave transformation, breaking and runup" provides a complementary physical foundation through the Serre–Green–Naghdi equations (Bonneton et al., 2010). The regime is fully nonlinear, $F(p;\phi)$01, and weakly dispersive, $F(p;\phi)$02. The paper uses a dispersion-improvement parameter $F(p;\phi)$03, high-order finite-volume and hybrid FV/FD solvers, and two different breaking treatments: explicit diffusive terms in SERR-1D and local degeneration to NSWE shocks in the hybrid scheme. Reported validations include strongly nonlinear cnoidal waves with relative amplitude error approximately $F(p;\phi)$04 and celerity error less than $F(p;\phi)$05 at $F(p;\phi)$06 m, as well as random JONSWAP waves over a mild-slope beach reproducing higher-harmonic generation, surf-zone dissipation, and infragravity transfer. This is directly relevant where SurfDesign denotes engineered surf or swash-zone conditions rather than molecular or fluid-object design.

A higher-fidelity free-surface alternative is SPH. "Numerical simulations of surf zone wave dynamics using Smoothed Particle Hydrodynamics" uses DualSPHysics in weakly-compressible form to simulate spilling and plunging breakers over a plane beach and a fringing reef (Lowe et al., 2020). Water is represented by Lagrangian particles, pressure is closed by Tait’s law

$F(p;\phi)$07

and surface tension, rollers, splash-up, and undertow emerge without mesh regeneration. A single numerical setup is used across all cases: $F(p;\phi)$08, $F(p;\phi)$09, and artificial viscosity $F(p;\phi)$10. The paper reports excellent agreement for wave-height evolution, setup, skewness, asymmetry, and undertow, with normalized RMSE approximately 0.037 for wave height, 0.091 for setup, and 0.104 for current in the TK94 spilling case. The authors explicitly position SPH as a design-refinement tool for artificial reefs and surf-amenity structures, with the caveat that 2DV high-resolution simulations remain computationally expensive.

Taken together, these works indicate that SurfDesign depends not only on a target-specific objective, but also on a geometric or physical substrate capable of representing surfaces faithfully enough for optimization, control, or interaction. Current usage therefore spans at least three technical regimes: surface-conditioned generation, differentiable surface-aware simulation, and intrinsic surface editing.