AcoustiPrint: Physics-Guided Neural Design of Manufacturable Acoustic Structures

Shanmuka Sadhu; Harshvardhan C. Takawale; Yehia Zakaria; Ahmed Allam; Nirupam Roy

cs.LGOct 21, 2026

AcoustiPrint: Physics-Guided Neural Design of Manufacturable Acoustic Structures

Authors: Shanmuka Sadhu, Harshvardhan C. Takawale, Yehia Zakaria, Ahmed Allam, Nirupam Roy

Organizations: Department of Computer Science, University of Maryland, College Park · Department of Mechanical and Materials Engineering, University of Cincinnati

Abstract

Recent work in additive manufacturing and neural inverse design enables the creation of complex three-dimensional structures to manipulate physical fields, yet these designs must also adhere to discrete, non-differentiable fabrication constraints. Current methods limit the design space by imposing differentiable soft manufacturability loss penalties, or by fixing structures through post-processing, causing a discrepancy between the geometry optimized by the physics model and the final fabricated result. Thus, we present AcoustiPrint, a physics-informed neural architecture for constrained inverse design that represents three-dimensional geometries with an implicit neural representation (INR) and passes each candidate through a printability operator before evaluating its final response. The printability operator executes layer-wise self-support, discrete material selection, and whole-body connectivity, assuring fabrication feasibility. To allow for backpropagation through the discrete non-differentiable operations, we use surrogate gradients for the backward pass and a self-supervised printability objective that progressively drives the INR toward a valid design domain. We demonstrate AcoustiPrint for personalized transcranial focused ultrasound, where inter-patient differences in acoustic properties and head geometry deform wave propagation and requires patient-specific acoustic focusing. AcoustiPrint jointly optimizes three-dimensional geometry and material composition through differentiable wave physics while ensuring manufacturability. Experiments show manufacturable acoustic structures with enhanced focal accuracy and over density-based and phase-based baselines, demonstrating a generalized methodology for neural design through non-differentiable manufacturing constraints and differentiable physics.

Figures & tables

Figure 1: Overview of AcoustiPrint . End-to-end optimization of printable acoustic geometries.

Method	Overlap (%)	Ratio (R/2R)	Shift (mm)	Peak P. (A.U)	RMS P. (A.U)
Unconstrained Ref.	32.5	1.848	0.98	2.34	0.763
AcoustiPrint	46.6	1.808	0.81	1.87	0.680
Homo. PAT	32.3	1.556	4.41	0.626	0.199
Hetero. PAT	22.2	1.795	0.90	1.05	0.416
Thickness	24.1	1.130	4.28	0.285	0.076
Sigmoid	27.5	1.615	1.82	0.867	0.276

Table 1: Main Results for Center Focusing. Average of CT-105, CT-166, and CT-260 results.

Figure 2: Normalized Pressure Difference of Printable(Top) and Unconstrained(Bottom) lenses before and after 3D Slicer.

Figure 3: Ablation Study of Differentiable and Non-differentiable components across four metrics: (a) Percentage of voxels removed, (b) Largest component fraction, (c) Number of supported components, and (d) RMS Pressure Focus

Freq(kHz)	Overlap (%)	Ratio(R/2R)	Shift (mm)	Peak P.(A.U)	RMS P.(A.U)
100	21.3	0.691	11.22	0.4298	0.2120
250	72.2	1.827	0.40	9.5500	4.4780
500	26.8	1.809	0.98	3.057	0.942
750	34.7	1.565	4.02	0.0642	0.0217

Table 2: Results for different transducer frequencies.

Location	Overlap (%)	Ratio (R/2R)	Shift (mm)	Peak P. (A.U.)	RMS P. (A.U.)
Center	26.8	1.809	0.98	3.057	0.942
Off-Center	42.7	1.821	0.98	1.777	0.66
Diagonal Off-Center	52.3	1.758	2.83	1.165	0.4719
Deep Center	44.3	1.865	2.83	1.905	0.7108
Shallow Center	49.2	1.774	2.04	2.763	1.071
Left Lateral	28.1	1.814	1.70	1.444	0.4616

Table 3: Effect of different focus locations.

Figure 4: Three letters: ‘S’(Left), ‘M’(Middle), ‘U’(Right).

Figure 5: Pressure Field Comparison COMSOL and j-Wave.

Figure 6: Acoustic Comparison among patients in our dataset for all 290 patients in our dataset. (a) Percentiles of acoustic speed(top), density(middle), and attenuation(bottom). (b) Log-scale of acoustic speed(top), density(middle), and attenuation(bottom) for both brain(blue) and skull(orange) across all patients. (c) Tissue(CSF, Brain, Trabecular Skull, and Cortical Skull) composition.

Tissue	Parameter	Mean	Std Dev	Min	Max
Brain Soft Tissue	Speed (m/s)	1549.6	7.1	1534.1	1569.5
Brain Soft Tissue	Density (kg/m 3 )	1039.6	5.3	1027.9	1054.5
Brain Soft Tissue	Attenuation (dB/cm/MHz)	0.550	0.000	0.550	0.550
CSF	Speed (m/s)	1518.7	1.1	1516.0	1523.0
CSF	Density (kg/m 3 )	1016.3	0.8	1014.3	1019.5
CSF	Attenuation (dB/cm/MHz)	0.020	0.000	0.020	0.020

Table 4: Acoustic property statistics for the 290 CT-scan dataset

Figure 7: a. Violin Plot of pairwise skull-surface chamfer distances b. Violit Plot of pairwise skull-volume Intersection-over-Union

Tissue	Mean (%)	Std Dev (%)	Min (%)	Max (%)
Brain Soft Tissue	73.96	3.30	64.38	82.51
CSF	6.93	2.78	2.60	17.51
Trabecular Skull	6.68	1.88	3.43	15.49
Cortical Skull	12.43	2.55	6.49	19.18

Table 5: Tissue composition statistics across patients

Figure 8: Density plots of Jensen-Shannon(y-axis) by IoU(x-axis) is plotted for all pairs with a. attenuation, b. density, and c. speed

CT-A	CT-B	Misfocus Dist. (center)	Misfocus Dist. (off-center)
105	11	11.172	22.706
260	318	21.995	29.593
166	308	12.189	19.640
281	29	7.673	21.269

Table 6: Misfocus distances(mm) for central and off-center focusing across different CT pairs.

Figure 9: Normalized pressure landscape (XY, YZ, and XZ slices) for 250 kHz (left) and 500 kHz (right).

Figure 10: Four different focus locations: a) Deep Center (top left), b) Shallow Center (bottom left), c) Right Lateral (top right), and d) Left Lateral (bottom right).

$\omega$	Overlap (%)	Ratio	Shift (mm)	Peak P.	RMS P.
30	22.9	1.835	0.89	2.588	0.750
60	23.8	1.830	0.69	3.315	0.968
90	28.0	1.815	0.69	3.218	1.008
120	28.0	1.793	0.89	2.777	0.877

Table 7: Ablation results for SIREN INR

\omega

$\tau$	Overlap (%)	Ratio	Shift (mm)	Peak P.	RMS P.
0.005	37.9	1.763	0.98	1.264	0.450
0.01	31.0	1.747	2.08	1.484	0.479
0.05	28.7	1.817	0.69	2.305	0.718
0.1	26.5	1.795	1.13	2.270	0.699

Table 8: Ablation results for Gumbel temperature

\tau

$\tau$	Overlap (%)	Ratio	Shift (mm)	Peak P.	RMS P.
0.01	35.9	1.756	1.26	1.441	0.496
0.05	29.9	1.771	1.33	1.560	0.523
0.1	32.5	1.781	0.89	1.579	0.523
0.25	30.4	1.765	0.98	1.524	0.496

Table 9: Ablation results for Sigmoid Gate hyper-parameter

\tau_{g}

$\lambda$	Overlap (%)	Ratio	Shift (mm)	Peak P.	RMS P.
0.01	32.0	1.736	1.70	1.429	0.4703
0.02	29.6	1.751	1.69	1.576	0.498
0.05	38.1	1.760	2.40	1.366	0.487
0.075	32.1	1.688	2.20	1.498	0.454

Table 10: Ablation results for Printability loss term hyper-parameter

\lambda

Method	Overlap (%)	Ratio (R/2R)	Shift (mm)	Peak P. (A.U)	RMS P. (A.U)
Unconstrained Ref.	41.5	1.822	1.55	1.29	0.469
AcoustiPrint	47.3	1.796	0.94	0.931	0.347
Homo. PAT	41.8	1.327	7.87	0.175	0.0337
Hetero. PAT	23.8	1.688	0.53	0.414	0.117
Thickness	31.5	0.986	5.52	0.100	0.0309
Sigmoid	42.8	1.586	2.58	0.331	0.119

Table 11: Main Results for Off-Center Focusing. Average of CT-105, CT-166, and CT-260 results.

Grid size	Overlap (%)	Ratio	Shift (mm)	Peak P.	RMS P.
1	55.9	1.760	4.04	1.771	0.746
2	40.1	1.704	1.44	0.503	0.169
4	28.6	1.814	0.57	1.997	0.623
6	26.8	1.819	0.57	3.508	1.065
8	27.1	1.814	0.69	3.205	0.978
10	32.5	1.848	0.98	2.34	0.763

Table 12: Results for different size grids of transducers.

%	Overlap (%)	Ratio	Shift (mm)	Peak P.	RMS P.
20	89.7	1.546	4.44	0.6089	0.3014
40	45.7	1.764	0.57	1.998	0.7804
60	32.5	1.848	0.98	2.34	0.763
80	20.4	1.858	0.89	3.573	0.9510
100	19.2	1.856	0.89	3.760	0.9837

Table 13: Results for varying transducer head coverage percentages.

Hyper-parameter	Unconstrained	Printable
Frequency	500 kHz	500 kHz
Optimizer	Adam	Adam
Optimizer steps	30	30
Learning rate	$5\times 10^{-4}$	$5\times 10^{-4}$
SIREN hidden units	128	128
SIREN depth	4	4

Table 14: Optimization hyperparameters used for unconstrained and printable lens optimization. Parameters not applicable to the unconstrained method are denoted by “–”.

Result	Modification
Table 2 (Frequency study)	Change --frequency .
Table 3 (Focus location study)	Change --focus-location .
Table 7 (SIREN initialization)	Change --siren-omega0 .
Table 8 (Gumbel temperature)	Change --gumbel-temperature .
Table 9 (Seed gate temperature)	Change --seed-gate-temperature .
Table 10 (Slicer penalty)	Change --slicer-penalty .

Table 15: Instructions for reproducing the quantitative results reported in the paper. Unless otherwise specified, all experiments use the default unconstrained configuration. Printable results are obtained by enabling the printability arguments listed in Table 14 .

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