## 2 Experimental Procedure  
The dendritic lattice structures were designed by a computer graphic application (Autodesk: Fusion 360), as shown in Figure 1a-d. The cylindrical lattices were connected at the nodal points with coordination numbers 4, 6, 8 and 12 and spatially propagated at equal angles. The lattice aspect ratios, defined as the numerical proportions of diameter to length, were systematically modified from 0.75 to 3.00 to maximize the specific surface area. The designed unit cells in the cubic envelopes were continuously arranged to create lattice structures with ordered porous patterns. All the cavity paths were continuously connected and diverged along the lattice coordination. The periodically formed nodal points had the same coordination number. The liquid phase streamlines were visualized by a computer fluid dynamics (CFD) application (Cybernet: Ansys Workbench). The pressure and temperature distributions at the surfaces and insides of the connected lattices were simulated using the finite element  
Figure 1: Graphic models of dendritic lattices in cubic unit cells. Cylindrical lattices were connected at coordination numbers of 4, 6, 8 and 12, as shown in (**a–d**), respectively. These units were continuously copied and parallel-translated in three dimensions to create the lattice propagations. method (FEM). In the calculation area, the dendritic structures with lattice constants of 3.54 mm were spatially arranged for 2 \(\times\) 2 \(\times\) 2 = 8 units, as shown in Figure 2. The molten salt of the aluminum and cryolite mixture was assumed to be a high-temperature fluid at 1000 \({}^{\circ}\)C. The density and viscosity were 2.75 g/cm\({}^{3}\) and 2.58 mPa\(\cdot\)s. The pressures at the inlet and outlet were 1.01 and 1.00 atm. No-slip conditions were applied at the liquid and solid interfaces. YSZ particles (DKK, HSY-0293) with an average diameter of 520 nm were dispersed into the acrylic resin (JSR, KC-1287) at a volume fraction of 45%. The formed paste was sealed in a polyester container with a capacity of 500 cc. The air bubbles were removed by centrifugal forces during revolution movements, and the particles and resin were kneaded in rotation movements using a mechanical mixer (SK-Fine, SK-350T). The rotation and revolution speeds were configured at 700 and 500 rpm. The batch processes with mixing times of 5 min were repeated for three sets. Subsequently, the paste material was packed into a syringe barrel with a capacity of 500 cc, and the syringe unit was mounted onto the STL-AM equipment (SK-Fine, SZ-2500). The paste material was injected from the syringe unit by pneumatic pressure and spread on a metal substrate using a mechanically movable knife edge. An ultraviolet (UV) laser with a wavelength of 355 nm was focused on a beam with a diameter of 50 \(\upmu\)m and scanned on the paste surface at a moving speed of 2000 mm/s. A testing film (edge length of 5.0 \(\times\) 5.0 mm) with a round hole (1.0 mm in diameter) was drawn, as shown in Figure 3. The irradiation power of the laser beam was increased from 50 to 250 mW to optimize the lithography conditions. The film thicknesses and hole diameters were systematically measured according to the irradiation power to estimate the curing depths and part accuracies using a digital optical microscope (DOM) (Keyence, VH-Z100). The sequential STL-AM process is schematically illustrated in Figure 4. The cross-sections were consecutively formed by the laser drawing through photopolymerization in the spread paste layers. The solid component was successfully fabricated by layer lamination and bonding under optimized lithography conditions. The unsolidified pastes were removed by compressed air blowing and ultrasonic washing. The obtained composite precursors were dewaxed and sintered at 1350 \({}^{\circ}\)C for 2 h in air. The relative density was measured using the Archimedes' method. The microstructures of the YSZ lattices were observed using a scanning electron microscope (JEOL, JSM-6060).