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
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).
ω
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 ω
τ
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 τ
τ
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 τg
λ
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 λ
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
5×10−4
5×10−4
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 .
Chair of Vibroacoustics of Vehicles and Machines, Technical University of Munich, Garching, 85748, Germany · Independent Researcher, Munich, 81377, Germany